School Size, Violence, Achievement and Cost

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School Size, Violence, Cost and Achievement
A Report of the Commission on Business Efficiency
of the Public Schools
Table of Contents
COMMISSION?S EXECUTIVE SUMMARY......................................................................... v
Source And Background .................................................................................................... v
Policy Problem................................................................................................................. vii
Methodology.................................................................................................................... vii
Samples And Data........................................................................................................... viii
Discussion Of The Theory................................................................................................. ix
Significant Findings ........................................................................................................... x
Recommendations........................................................................................................... xiv
Summary Of Other Appendicies...................................................................................... xvi
REPORT OF DR. RUSSELL S. HARRISON.......................................................................... 1
Acknowledgements............................................................................................................ 2
An Introduction To The Debate.......................................................................................... 3
A Historical Perspective ............................................................................................... 3
Prior Empirical Research On Test Scores ..................................................................... 7
The Need For New Research .................................................................................. 8
Why The ?Harrison? Research Methodology Produces Superior Estimates................... 8
Prior Research On Other Endogenous Outcomes: ....................................................... 10
The Need For New Research ................................................................................ 12
Why The New Research Design Is Superior To Prior Estimates............................ 13
Prior Research On Inefficiency And Loss Of Productivity.......................................... 14
The Need For New Research ................................................................................ 15
Summary Of Research Findings ....................................................................................... 16
Detailed Proofs And Explanations.................................................................................... 17
Summary Of Detailed Proofs And Explanations............................................................... 21
Section 1 ? School Size And Achievement....................................................................... 22
Section 2 - School Size And Violence .............................................................................. 29
Section 3 - School Size And Cost ..................................................................................... 39
Section 3a: The Custodial/ School House Function Versus The Educational/ Value
Added Function Comparing Two Types Of Cost/Benefit Ratios As A Function
Of School Size:..................................................................................................... 42
Section 3b Linkages From School Size To The Costs Of ?Housing? Students - Schools
Housing 500-999 Students Have Significantly Lower Total Costs Per Pupil ......... 52
Section 3c A Closer Look At Four School Cost Indices For Very Big Schools Of
1,500 Or More Students........................................................................................ 61
Section 4: - ?Compounded? Inefficiency And ?Residual? Inefficiency ............................. 71
Section 4.4 - The Need For Even More Compelling Evidence ................................... 77
Section 5 - Where To Find The Evidence ......................................................................... 80
Section 5a Selecting The Sample,............................................................................... 81
Section 5b: Sources Of Data Used To Produce Tables ............................................... 85
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Section 5c: Description Of Samples Used In Various Tables -Criteria For Selection... 87
Section 5d: The Number Of Cases In Each Table ....................................................... 89
Section 6 Summary Of Key Variables And Concepts ....................................................... 93
6a: Variables Used To Explain Differences In Test Scores In Section 1...................... 94
6b: Variables Used To Explain The Geographical (Spatial) Concentration Of Violence
Within A District In Section 2 .............................................................................. 95
6c: Variables Used To Explain Differences In Compounded Inefficiency Among NJ High
Schools In Section 3 ............................................................................................. 96
Section 6d: Key Concepts.......................................................................................... 97
Section 7 ? Key Readings On Methods .......................................................................... 102
Section 8 ? Key Research............................................................................................... 108
Section 9 - Implementation ............................................................................................ 114
Section 10 - Followup Research ..................................................................................... 119
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School Size, Violence, Cost and Achievement
A Report of the Commission on Business Efficiency of the Public Schools
Commission?s Executive Summary
SOURCE AND BACKGROUND
The Commission on Business Efficiency of the Public Schools responds to
requests from members of the Legislature as well as from its direct members.
Assemblyman Louis Greenwald asked the Commission to consider examining the
relationship of school size and violence in order to determine if there exists a causal link
between the variables. The Commission discussed this issue and determined that there
was a possibility of a significant link between school size and violence. However, the
members of the Commission were concerned that an analysis of these two variables alone
might lead to conclusions which would a) negatively affect other important public values
and b) provide an incomplete picture leading to inappropriate decision making. The two
values the Commission believed most likely to be negatively affected by decisions based
on an analysis of size and violence alone were student achievement and cost. As a result
the Commission decided to include achievement and cost in the examination. Further the
Commission thought that if a link exists and it is sufficiently significant, this link might
be important on a policy level at this time in New Jersey. Currently, school districts in
New Jersey are in the process of building new schools as a result of a recent building
bond in excess of $8 Billion. The Commission felt that information regarding school size
and how it affects school performance and operation could be valuable to decision
makers at both the local and State levels.
In the past examinations of size as it relates to New Jersey education has focused
primarily on district size and class size. School size has not received significant attention
from policy makers. The studies on district size have had mixed results. Some studies
have suggested that district size should be increased to realize benefits from economies of
scale. Other studies have suggested that the economies of scale, if they exist, may be
offset by diseconomies of performance. Still other studies (including one by the
Commission) have suggested that many of the benefits of economies of scale can be
achieved through increased cooperation between and among districts and other
governmental entities in the form of shared services.
The validity of these studies not withstanding, regionalization of small school
districts into larger ones seems to have reached a plateau in New Jersey. If structural
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changes toward efficiency are to be made in the near future, it seems unlikely that they
will take the form of increased regionalization.
In New Jersey, public elementary and secondary education is a major budget
issue. At the state level, it claims more than $8 billion of the state budget (2004 fiscal
year projected). At the local level, taxpayers contribute an additional amount in excess of
$10 billion annually.
Though funding has dramatically increased, so have recent reports of violence in
many districts. Problems of absenteeism and dropouts continue to plague far too many
schools. Achievement has remained largely unchanged. While the problems underlying
these issues seem, to some, immutable, the Commission believes that it is important that
the State continually seeks to identify, articulate and solve such problems. Failure to do
so would be irresponsible.
Recent research indicates that at least a part of the solution to these problems lay
in the size of individual schools. In some studies small schools appear to be producing
lower violence, higher achievement and may contain cost advantages as well.
The basic questions for this study deal with the relationship between and among
these variables. Specifically, is there a relationship between and among the independent
variable school size and the dependent variables violence; achievement; and cost?
To answer these questions the Commission contracted with Professor Russell
Harrison of Rutgers, the State University.
Under the direction of the Commission, Professor Harrison (1) conducted an
initial review of the research literature in academic journals, books, and research reports
to understand the current thinking regarding school size, violence, achievement and cost;
(2) evaluated alternative definitions of school size, violence, achievement and cost; (3)
collected, analyzed, and evaluated the data available at the state level on these variables
to determine if a sufficient relationship exists to warrant further and more extensive
research and (4) prepared the research findings in a form that is useful in the education
debate.
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This resulting report serves as a preliminary examination to determine if more
detailed study is warranted.
POLICY PROBLEM
The problem addressed in this paper is to investigate and identify possible
alternative organizational approaches, which may help to improve the efficiency and
effectiveness of New Jersey Public Schools. Specifically the issue addressed is to
determine if sufficient evidence exists to recommend that the Legislature seek to
encourage smaller school size. In this context school size means the size, in pupils, of
organizational units providing direct education services to a defined group of children. In
common language: the number of pupils who attend an individual school. Here, a school
is usually a school building, but may also be a school-within-a-school. A school-withina-
school exists where multiple, separately, administered schools exist within a single
school building.
METHODOLOGY
In conducting the research the contractor was directed to determine, at the 95%
confidence level, if there exists a relationship between and among the independent
variable size and the dependent variables violence, cost and achievement. In research
terms, the contractor was asked to seek to prove that any relationships between or among
school size, violence, achievement and/or cost are coincidental (the null hypothesis).
Failing to prove that at the 95% confidence level, he was to reject this theory in favor of
the conclusion that these relationships do indeed exist and to explain the direction of the
relationship (positive or negative).
In conducting the research publicly available data relative to each of the variables
were used. The statistical analysis was performed by measuring differences in mean
values of the dependent variables for different values of the independent variable,
analysis of variance for those differences, and multiple regression analysis.
The research regarding violence and achievement was limited to high schools due
to the quality of data available regarding achievement and violence. Another reason for
this focus is that problems of anomie and alienation have serious consequences in high
schools. Student violence and school crime literally become matters of life and death.
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Moreover, high school students are more apt to skip school or be absent on their own
volition. They are also more likely to get into major problems with the law while playing
hooky than elementary school students. Thus both misbehavior in school and
absenteeism from school can have serious immediate consequences for high school
students.
The combination of poor grades and dropout risks are also serious problems in
high schools. In high school, far more so than earlier grades, students performing poorly
or missing class are much more likely to leave school. Poor grades, absenteeism, and
dropouts push students off the ladder to middle class prospects into a culture of poverty
from which escape is difficult. In the culture of poverty they face a morass of problems
for themselves and for society as a whole. Areas with more dropouts are especially prone
to suffer from other non-school related problems like births to unmarried females,
homicides that lead to incarceration in adult prisons for males, deficient care for children,
both unborn and born, and elevated risks of infant death. Tax payers may face extra costs
for public health care and corrections where dropout rates escalate.
Data on costs included both high schools and all schools.
SAMPLES AND DATA
As mentioned above the samples used in this report for achievement and violence
were restricted to high schools. For each analysis a different sample was used to
demonstrate that the effects were not dependent on a single sample. Details of the
samples are included in the appendices.
The HSPT passing rates for each of the three parts of the test (math, reading and
writing) were used as surrogate measures of achievement.
Statistics gathered by the New Jersey Department of Education in 2000 were used
to measure violence, which included the most serious school incidents.
The cost measures used spending per pupil from the various school years as
reported by New Jersey Department of Education in its State Report Card. District
spending was used due to the lack of available data for individual schools. Several
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different cost measures were also constructed to measure educational value received per
dollars spent.
DISCUSSION OF THE THEORY
What is the relationship of school size with school crime, poor test scores, and
inefficiency in educational service delivery? Does a careful review of evidence for a
sample of New Jersey schools produce findings sufficient to show that any apparent
relationships between the variables is more than coincidence?
Communities face special problems where problems of academic failure, low test
scores, student violence, school crime, absenteeism, dropouts, are combined with inflated
school budgets. Parents of high school students tend to have a longer earning record and
larger savings than parents of elementary children. They are more apt to own or consider
home ownership, and are especially sensitive to local tax burdens to fund schools. If
schools are both expensive and ineffective, they are apt to vote ?with their feet?. Parents
of high school students are especially prone to flee an inefficient school system,
especially where options are close at hand.
This loss of middle class families from the school and the larger community
further compounds the problem of academic progress for those left behind, and impedes
the realization of vital educational goals. Thus endogenous educational problems
produce a downward spiraling cycle of mutually reinforcing educational failures.
Many variables shape educational problems. However, this research was
designed to test a theory that school size is a major exogenous variable shaping the
endogenous problems that plague many public school systems, including high schools.
If this theory is valid, then large schools and school size should be seen as major
explanations for differences in overall inefficiency at the high school level. To the extent
relationships of school size with inefficiency problems are highly significant, then public
officials in New Jersey should take heed in future debates about educational best
practices, optimal architectural design, and rational planning for education governance
and administration.
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SIGNIFICANT FINDINGS
Following are the significant findings of this preliminary examination as they
relate to each of the dependent variables achievement, violence and cost.
Finding I Small schools have significantly higher test scores than large schools.
One task for this project was to estimate relationships of school size with test
scores on High School Proficiency Tests (HSPT). The tests measure student success in
mastering math, reading, and writing skills respectively.
Passing rates on the three tests were dramatically higher depending on the size of
the school. For instance, the passing rate on the math portion of the HSPT was 9.5
percentage points higher, on average, in schools with 500 or fewer pupils than in schools
with 1500 or more pupils. The differences in writing and reading were 9.1 and 14.5
percentage points respectively. The results are found in Section 1 of the Full report.
Finding II Small schools have significantly less violence than large schools.
In estimating the relationships of school size with student violence and school
crime, data from the New Jersey Department of Education?s ?Violence, Vandalism and
Substance Abuse in New Jersey Schools ? 1999-2000? was used. The evidence is clear,
looking at a sample of high school districts in New Jersey.
The size of district schools is positively correlated with the concentration of
student violence and school crime in a given district. This result is analogous to prior
research on school segregation. This study shows that school size is also significantly
correlated with the concentration of violence and crime in one district versus others. The
size of the average school in each district is significantly correlated with violence and
overall criminal incidents for districts serving a majority high-school students.
Using a tipping point for school size of 1000 pupils, small schools on average
(mean and median) experience between 29 to 40 percent fewer incidents of violence than
do all of the schools in the sample. Schools with more than 1000 pupils experience
between 58 and 108 percent more incidents of violence. The results are found in Section
2 of the Full report.
Finding III Expenditures per pupil vary with school size and type.
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Step 3 of this project was to examine available data to determine (1) if a
relationship exists between school size and fiscal cost, and (2) what the nature of that
relationship is if it exists.
Note: This part of the analysis uses direct school expenditures only. Costs external to
the school district are examined later in the report and discussed in other findings.
In general expenditures on a per pupil basis for smaller high schools were higher
than the costs of larger schools. However, the variance in districts of all types (including
elementary and middle schools) was far from a simple straight line.
The data related to the following sub findings can be found in TABLE 3A2:The
ratio of fiscal costs in a given year on page 46 of the full report.
Finding III a. Small high schools with less than 500 pupils have higher expenditures
for operation on a per pupil basis than large schools and lower expenditures per
pupil than schools in the 500 to 999 range.
High Schools under 500 pupils experienced costs per pupil 1.4 percent higher
than the mean for the all high schools in the sample. This represented a difference of
$117. These schools had expenditures $726 per pupil higher when compared to high
schools with more than 1500 pupils representing a difference of 9.5 percentage points
around the mean.
This shift in difference in cost when compared to the difference in achievement
may indicate that the most efficient high school size is somewhere near or below 500
pupils. However, this is examined in more detail later in the report.
Finding III b Small high schools with 500 to 1000 pupils have significantly higher
expenditures for operation on a per pupil basis than schools with 1,500 or more
pupils.
High Schools with 500 to 999 pupils experienced costs per pupil 2.8 percent
higher than the mean for the all high schools in the sample. This represented a difference
of $233. When compared to high schools with more than 1500 pupils these schools had
expenditures 11.0 percent higher representing a difference of $842 per pupil.
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Finding III c. Small schools with less than 500 pupils have higher expenditures for
operation on a per pupil basis than large schools.
When the focus is shifted to include schools at all levels, the variances are much
different. Schools under 500 pupils experienced costs per pupil 3 percent higher than the
mean for all schools in the sample or $243 per pupil. On a percentage basis this is a
larger gap than for the same population class in high school only comparisons. However,
when compared to all schools with more than 1500 pupils the difference shifted from 9.5
percent in the high school comparison to 8.8 percent in the all schools comparison. This
8.8 percent difference represents a $665 per pupil difference.
Finding III d. Schools with enrollments between 500 and 1000 pupils have slightly
higher expenditures for operation on a per pupil basis than large schools.
The difference between schools with 500 to 1000 pupils and was only 0.5 percent
or roughly $35 per pupil higher than those with 1500 or more pupils. This class of
schools had expenditures lower, in this comparison, than both the smallest schools and
those schools with enrollments between 1000 and 1500.
The significance of this is the indication that optimal school sizes are likely
different for schools of different types. That is an ideal size range for a K-6 school is
different that for a high school.
One possible explanation is simply that small schools with 500-1000 students face
fewer of the unique challenges of the other even smaller schools serving fewer than 500
students. To house their students and meet their challenges, schools with 500-999
students do not have to spend a lot more than other schools. In fact, they spend a lot less
than other schools.
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Finding IV Small schools have significantly higher value per dollar spent than large
schools.
While the cost of educating a student in varying sizes of school is valuable, it is
important to examine the other social values realized by schools in combination with the
immediate fiscal cost.
Step 4 of this project was to examine the interrelationships of all four variables
under examination in this study simultaneously in order to understand the cost/benefit of
changes in schools size. To accomplish this, several approaches were used.
(1) Four separate indices were constructed to show fiscal cost, cost
adjusted for expenditures by other governmental units incurred
relative to dropouts, cost (through enrollment adjustments) of
increasing proficiency test passage rates, and costs adjusted for both
dropouts and passage rates.
(2) Construction of ?Composite Inefficiency? scores to measure not only
fiscal costs but also social and academic costs and to measure than
over time.
The approaches use varying enrollment break points to examine the sensitivity of
the results to differing groupings of enrollment size. These measures show consistently a
higher value achieved per dollar spent for smaller schools.
Parts of Section 3 and Section 4 of the full Report demonstrate these results.
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RECOMMENDATIONS
While the Commission finds that there are significant fiscal and social advantages
to smaller school size, the Commission also finds that the current research is insufficient,
for the most part, to support specific policy recommendations. Additional research
should be done before specific school size recommendations can be made. However, the
Commission also believes that sufficient proof has been shown to warrant both additional
research and serious consideration by school districts embarking on construction projects
of the planned capacity of those projects
Action Recommendations
Recommendation One: The research indicates that, in High Schools, a cost/benefit
tipping point exists somewhere between 500 and 1,000 students. While further study
should be done on this topic, districts considering school sizes significantly higher than
1000 should consider multiple small schools as opposed to large single schools.
Recommendation Two. School districts with existing high school facilities or which are
in the process of constructing facilities with enrollments over 1,000 pupils should study
the feasibility of creating separate administrative units (known as ?schools within
schools?) within these school buildings.
Research Recommendations
Recommendation Three. Studies should be conducted to identify separate, useful
enrollment targets for elementary, middle and high schools. These studies should take
into consideration the costs, both direct and indirect of 1) facilities and maintenance, 2)
achievement and 3) violence.
Recommendation Four. A study should be conducted to examine the relationship of
school size to problems affecting middle school and junior high school students in
particular, including failures on GEPA tests, school crime and violence, school climate
and performance in high school.
Recommendation Five. A study should be conducted to examine and analyze
nationwide surveys to link school size with the costs of construction, maintenance, and
transportation
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Recommendation Six. A study should be conducted to examine and analyze nationwide
surveys to link school size, parental alienation, and lack of involvement by parents in
elementary middle and high school levels.
Recommendation Seven. A study should be conducted to examine and analyze
nationwide surveys that link school size with the loss of consensus and rapport between
teachers and principals
Recommendation Eight. A study should be conducted to examine and analyze
nationwide surveys that link school size with physical conflicts and fear as problems
facing schools
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SUMMARY OF OTHER APPENDICIES
Section 5 of Report 2 summarizes the key variables used in the present research,
and section 6 summarizes key concepts used in regression analysis and hypothesis
testing.
Section 7 provides background readings on research methods, and section 8
outlines prior research studies relevant to school size outcomes and implementation
options.
Section 9 outlines the range of implementations strategies that deserve close
attention, and section 10 emphasizes specific research issues that merit and deserve
separate follow-up study and analysis.
Report of
Dr. Russell S. Harrison
Linkages
Between School Size and
Adverse Educational Outcomes in New Jersey ?
Evidence of
Failing Test Scores,
School Violence,
And Inefficiency Costs
Report to the
Commission on
Business Efficiency of the Public Schools
Members of the Commission
Assemblywoman Arlene Friscia
Chairman
Laurie Fitchett
Vice-Chairman
Senator Diane B. Allen
Senator Shirley Turner
Assemblyman Samuel D. Thompson.
Ms. Tracy DiFrancesco
Mr. Thomas Niland
Dennis Smeltzer
Executive Director
Russell Harrison - Report on School Size and Education Outcomes - Page 2
ACKNOWLEDGEMENTS
Special thanks are due to Assemblyman Louis Greenwald who encouraged me and
endorsed the study, Assemblywoman Arline M. Friscia, Chair of the Commission on
Business Efficiency of the Public Schools and the other Commission Members, who
sponsored the study; as well as Dennis Smeltzer, Executive Director of the Commission,
who coordinated the study.
Russell Harrison - Report on School Size and Education Outcomes - Page 3
An Introduction to the Debate
And a Summary of Empirical Results for New Jersey
By Dr. Russell S. Harrison1
In New Jersey leading legislators like Assemblyman Louis Greenwald and
members of the Commission on Business Efficiency of the Public Schools are concerned
with problems of violence, poor achievement, and apparent inefficiencies that plague too
many schools and they children they serve. This report was produced to clarify how
small school learning communities can help alleviate some of these problems. More
specifically, it was designed to document the extent to which school size is correlated
with failing test scores, school violence, and inefficiency costs.
Whatever may have been true for the New Jersey of yesterday, what is the
evidence for New Jersey in recent years?
A HISTORICAL PERSPECTIVE
In the first half of the twentieth century certain educators advocated district
consolidation and the construction of bigger schools as a key way to improve educational
efficiency. Many based their hypotheses on evidence from industrial production studies.
It appeared that larger plants had declining marginal costs per ?widgets? produced, and
therefore displayed ?economies of scale?. Advocates of big schools assumed that
increased size was part of the package of ?scientific principles? and ?best practices? that
equally applied to big factories and big schools. Big schools were required to produce
students in the most efficient manner possible, to meet the needs of the new century, the
new industrial era, and a new bureaucracy paradigm.2
Proponents of the ?factory model? school agreed with Elwood P. Cubberley and other
urban reformers 3. He was a former urban school superintendent, and he wanted rural
schools built on the big city model. He advocated schools run on the new industrial
paradigm to encompass hundreds or even thousands of students, even though many of
those students still lived on the farm and roads were dangerous. Early in the century
Cubberly wrote:
Our schools are, in a sense, factories in which the raw products (children) are to be
shaped and fashioned into products to meet the various demands of life. The
specifications for manufacturing come from the demands of the twentieth century
civilization, and it is the business of the school to build its pupils to the specifications
laid down. This demands good tools, specialized machinery, continuous
1 As Consultant Dr. Harrison has worked with a wide range of federal, state, and local government
agencies, and works closely with leading South Jersey legislators.
At Rutgers University Dr. Harrison holds dual appointments as tenured associate professor both in
the Political Science Department and the graduate Department of Public Policy and Administration.
Previously he has served as Director of the Rutgers University Forum for Policy Research, and Chair of the
Political Science Department (twice). He heads the Political Science Internship program, teaches courses in
Research methods and State and Local Government politics and administration, lectures and writes on
Government Programs for Children and Youth, including Inequality in Public School Finances and other
issues of education reform and community-based service delivery.
2 R. E. Callahan, Education and the Cult of Efficiency. Chicago: University of Chicago Pres, 1972).
3 Elwood P. Cubberley, Rural life and education: A study of the rural-school problem as a phase of the
rural-life problem [New York: Houghton-Mifflin, 1915, Revised edition 1922; ERIC Document
Reproduction Service No. ED 392 559.
Russell Harrison - Report on School Size and Education Outcomes - Page 4
measurement of production to see if it is according to specification, the elimination of
waste in manufacture, and a large variety in the output.4
Proponents of the factory model school wanted not just a large school. They
idealized the Max Weber style of bureaucracy characteristic of large factories and other
industrial- age institutions. They wanted standardization, a top-down flow of commands,
no deviation from written rules and procedures, little improvisation, management but not
leadership, minimum influence from the community, maximum power for professional
elites over citizens and students. They favored ?authoritarian supervisory bureaucratic
rules and regulations?.5
Not just top-level school administrators enforced the new regime. Increasingly union
leaders responded to the sense of alienation felt by teachers in such schools. In the large
schools, teachers were not personally known to administrators or to each other, much less
to parents. Often they exercised only limited influence over major curriculum, hiring,
salary, or disciplinary decisions. Thus they asked their professional unions to promote
standardized treatment and add ?red tape? to protect teachers from authoritarian
personnel policies, or simply from being ignored.6
In turn organizational behavior research by Peter M. Blau and others confirmed that
organizational size and the adoption of bureaucratic rules and regulations were positively
correlated, not just in private industry but also in the public sector. Moreover, in the
absence of lateral power relationships, ?gangplanks? among teachers in different
departments, and the breakdown in communications inherent in large-scale organizations,
efficiency suffered.
As late as the 1950s and even the 1960s perhaps the bulk of research into the
consequences of organizational size and bureaucracy tried to document their superiority,
as an alternative to small-scale operations and informal social controls. Prominent
among them was James Bryant Conan. He was the former President of Harvard, a
chemist, and good friend to fund sources like the Carnegie and Ford Foundations that
favored big schools at the time. He tried to document the virtues of size and scale with
empirical evidence. For popular support, he played on public fear and envy of a Soviet
empire that seemed ahead in math, science, Sputniks, and centralized schooling. In turn
major foundations used Conant?s research to pressure for larger schools nationwide,
including mega-schools in New York City and other big cities.
The reports by James Bryant Conant illustrate the bias of the era. He surveyed small
samples of high schools, using very crude indicators collected by different interviewers in
different schools. From his small ad hoc sample he found that on average, larger schools
had more physical resources (namely, more teachers and more classes and more courses).
In turn he assumed that more physical inputs must lead to better quality outputs from the
educational process. He assumed that the multiplier effects of inputs like the number of
courses are directly correlated with academic success. He concludes that larger schools
4 For a telling commentary on the Cubberly paradigm see Evans Clinchey, Creating New Schools: How
Small Schools are Changing American Education, New York City: Teachers College, Columbia University,
2000, pages 7-8. See also Craig Howley, ?Ongoing Dilemmas of School Size: A Short Story?. ERIC
DIGEST, Eric Clearinghouse on Rural Education and Small Schools, October 1996. EDO-RC-96-6, pages
1-2.
5 See Evans Clinchy, ?Introduction: The Educationally Challenged American School District,? in Creating
New Schools, op cit., pages 8-9
6 Idem.
Russell Harrison - Report on School Size and Education Outcomes - Page 5
are superior. In particular, he argues that large ?comprehensive? high schools are
essential to meet the needs of the gifted and talented, like those who would later attend
Ivy League schools like Harvard. He systematically ignored issues about what was best
for the average student, much less the bottom tier student. The arguments by him, the
Ford Foundation, and others convinced many that big schools were best for high school
students, whatever their demerits for smaller, younger children.
In the absence of systematic data on test scores, or discipline problems, or school
crime, or other academic ?outputs?, common sense seemed to confirm the expectation
that bigger was always better. The public ignored the limited data base on which Conant
relied, the limited range of schools he studied, the fact that courses in small schools
varied little from the large schools, and the absence of outcome data to justify
conclusions about the impact of school size on actual student learning.
However, the last few decades of the 20th century brought major changes. A
growing volume of empirical data measured outcomes, not inputs, and not just for a grab
bag of schools. Systematic ?report card? data were popularized first through nationwide
samples, then for states, later by district, and eventually by school. The public and
politicians were able to look at empirical outcomes from K-12 education, to see more
clearly where students did better and why.
Among the first countries collecting and publishing ?report card? data were
Commonwealth countries like England and New Zealand. Under welfare state
governments they had achieved highly centralized financing combined with centralized
testing and centralized standards, run by national officials. They developed extensive
data files and record keeping systems that covered not just inputs like spending per
student, class size, ethnicity, and income, but also outputs like test scores and
absenteeism and suspensions.
New political leaders both of the left and right began to review such data. In turn
these leaders were among the first to perceive potential payoffs from a more
decentralized system of service delivery for K-12 education, including more site-based
decision-making, and alternative service delivery. Support was given to the use of
smaller schools under various forms of governance, and an end to ever growing
consolidation and centralization. Devolution of administrative control and ?the new
public management? became popular even before the Reagan era in the United States.
In the United States, cross-national data from the early NAEP and TIMSS tests
finally became widely available. These reports showed that the United States was
experiencing problems, comparing average U.S. test scores for the nation as a whole
versus other comparable countries during the early 1980s. This led to nationwide efforts
to combat educational problems for ?A Nation At Risk?, including national educational
goals.
By the late 1980s the NAEP tests began to produce report cards for individual
states. So did a wide range of individual states like California. The growing volume of
empirical evidence began to erode old complacencies about mega schools, and suggest
new priorities for reform.
During the 1970s and 1980s state supreme courts had enthusiastically embraced a
policy of judicial activism. In school policy, they had little access to outcome data. Thus
in their zeal to produce equality of inputs, they ignored issues of efficiency of outputs.
Russell Harrison - Report on School Size and Education Outcomes - Page 6
Dozens of state Supreme Court decisions mandated dramatic increases in state funding
for schools. Courts went on to prescribe where, when, and how that money should be
spent, including new construction.
However, states with more extensive involvement in the ?public school finance
reform crusade? often saw state taxes increase far more rapidly than student test scores.
Indeed, often the states with the most extensive litigation had the highest ratio of costs
per student to test scores. Inefficiency seemed quite common, to the extent that state
courts increased centralized funding for schools in states with consolidated districts
and/or consolidated schools. In the absence of concern for issues of organizational size,
states too often saw an unholy combination of high expenditures per student combined
with low test scores and increasing evidence of anomie and alienation within larger
schools.
Beginning in the late 1980s, and increasingly during the 1990s, many districts,
cities, and states began to consider new principles of architectural design and governance
to administer public schools. The ?new urbanism? encouraged a new commitment to
community-based schools. Principles of ?the new public administration? and
?reinventing government? encouraged movement away from the older status quo. A
concern for site-based decision-making and more responsiveness to what parents wanted
for their children brought new appreciation for small schools.
Support for small schools had always been strong in rural and suburban areas.
Now support for small schools grew in cities where liberal journalists reported that the
largest schools were little more than ?Dickensian workhouses breeding violence,
dropouts, academic failure and alienation? whereas ?schools limited to about 400 usually
have fewer behavioral problems, better attendance and graduation rates, and sometimes
higher grades and test scores?.7
Administrative ?leaders? and educational entrepreneurs in New York, Boston,
Chicago and other big city systems experimented with small schools. Qualitative
research and journalistic reports claimed favorable academic and non-academic outcomes
from these experiments with smaller schools. Advocates included Deborah Meier in
New York 8. the Coalition of Essential Schools and the ?pilot school? movement in
Boston 9, and in Chicago the Consortium on Chicago School Research and the Small
Schools Work Shop.
7 Susan Chira, ?Is Smaller Better? Educations Now Say Yes for High School,? New York Times,
Wednesday, July 14, 1993, p. A1.
8 Deborah Meier, The power of their ideas: Lessons for America from a small school in Harlem. Boston:
Beacon Press, 1995.
9 Evans Clinchy, editor, Creating New Schools: How Small Schools are Changing American Education,
Columbia University Teachers College, 2000.
Russell Harrison - Report on School Size and Education Outcomes - Page 7
PRIOR EMPIRICAL RESEARCH ON TEST SCORES
Using Multiple Regression Analysis of Cross-sectional Quantitative Data
For specific schools and districts
Friedkin and Necochea launched a bold new genre of empirical research in 1988.
10 They grounded their predictions about the effects of size on prior research into generic
organizational behavior. They did not limit their ideas to what they had seen on the job
as participant observers in a specific school or district. They developed and tested formal
hypotheses. They did not simply articulate and illustrate a journalistic thesis or policy
preference. They went beyond traditional case study conclusions, based on anecdotal
evidence for a specific school or district. Instead they used cross-sectional used data for
each district and school in an entire state. For data they looked to California, one of the
few states at the time with easily accessible data on test scores, poverty, school size, etc.
They used multivariate regression analysis to measure relationships, and clearly spelled
out how they measured each variable. They stressed objective evidence, not subjective
impressions.
They found that large schools and large districts ? and especially poverty districts
- have more students with special needs and behavior problems and ?culture of poverty?
traits. More importantly, they controlled for socio-economic status and measured the
independent impact of school size and district size on test scores. They found favorable
academic outcomes from smaller districts and from smaller schools, at least at lower
grades.
In accord with their ?contingency theory?, small schools in poverty communities
especially helped academic test scores. As large schools proliferated, and average size
increased, test scores went down, especially in communities where parents had little
education and low occupational status.
A growing number of subsequent studies by Craig Howley and Howard Bickel
showed similar results for states besides California.11
They have focused on heavily rural and poor states in the West and South. They
report that a combination of large schools and extreme poverty, measured variously, are
10 Friedkin and Niccochea, ?School system size and performance: A contingency perspective?.
Educational Evaluation and Policy Analysis, Vol 10, Issue, 3, 237-249.
11 See the following:
?Craig Howley, 1994 ?The Academic effectiveness of small scale schooling (an update).? ERIC
Digest. Charlestown WV. ERIC Clearinghouse on Rural Education and Small Schools. ERIC
ED 372897, Document Reproduction Service ED 389 503.
?Craig Howley, 1996, ?Compounding disadvantage: consolidation and the effects of school and
district size on student achievement in West Virginia.? Journal of Research in Rural Education,
Vol. 12, Issue 1, 25-32.
?Craig Howley, 2000. ?Effects of Poverty on Student Achievement Countered by Georgia?s
Smaller Schools.? Washington DC: The Rural School and Community Trust.
?Craig Howley and Robert Bickel, 2000. ?Results of a four-state study: Smaller schools reduce
harmful impact of poverty on student achievement?. Washington DC: Rural School and
Community Trust.
?Craig Howley, Marty Strange, and Robert Bickel. 2000. ?Research about school size and school
performance in Impoverished communities. ERIC Clearinghouse on Rural Education and Small
Schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 8
negatively correlated with academic test scores ? especially in lower grades. Using the
same methods as Friedkin and Niccochea, they find similar results.
The need for new research
Looking at the old and new empirical research on test scores and academic
outcomes by grade level, a recent study mandated by the state legislature in North
Carolina concluded that:
With respect to achievement, studies at the elementary level have consistently
found that smaller schools are associated with higher academic achievement. At
the high school level, the findings are more mixed. Some high school studies have
found higher achievement among students attending smaller schools, while others
have found no achievement advantage for small schools. Others have found that
students from medium-sized high schools outperform students from either smaller
or larger schools. There is also some evidence indicating that smaller schools are
particularly beneficial for students from economically disadvantaged
backgrounds. Overall, it would appear that smaller schools are associated with
higher achievement in elementary schools, but this conclusion cannot be stated as
confidently for high schools.12
However, very little research has focused on outcomes in a state like New Jersey,
looking at links from school size to academic outcomes for the 1990s. Thus the Harrison
report for the New Jersey Commission on Business Efficiency in the Public Schools is
critical. It documents a new era for New Jersey, beginning in the 1990s. After years of
public school finance reform litigation, variables separate from resources are coming to
the fore. Specifically, the correlation of school size and test scores is highly significant ?
even looking specifically at high school students. Big schools mean lower test scores,
including HSPT scores.
Why The ?Harrison? Research Methodology Produces Superior Estimates
[By Using Exogenous Institutionalist Prediction Models
Like those Cited In Sections 7 And 8]
One reason for the significant results is that the ?Harrison? research methods are
more refined than the prior research by Friedkin, Niccochea, Howley, and Bickel.
Friedkin and Niccochea concede that one reason that school size appears to help
academic outcomes is the linkage of school size to resources. Large schools often have
superior resources, in fact, a ?munificence? of resources, at least in aggregate. These
include a larger budget, more teachers, larger facilities, than for small schools. They
often have larger expenditures per student than smaller districts, especially in nonmetropolitan
areas. To the extent that big budgets facilitate small classes, and both
resources help performance, big schools will appear to be superior.
The result, however, is spurious. It is not due to the size of big schools but to the
resources their political clout allows them to amass as a base, and budgetary
incrementalism that keeps expanding their budgets by a given percent increment even in
the midst of problems.
12 State Board of Education, Department of Public Instruction, Office of Instructional and Accountability
Services, Division of Accountability Services, Evaluation Section, ?School Size and its Relationship to
Achievement and Behavior?, April 2000.
Russell Harrison - Report on School Size and Education Outcomes - Page 9
Such an admission would seem to demand a ?control? for spending, or perhaps
class size, which is a product of spending for teachers. However, prior research fails to
control for spending per student or class size when it links school size to test scores. The
Harrison research does, and it finds significant relationships linking school size in New
Jersey to HSPT test scores for math, science, and reading, ?ceteris paribus?.
The Harrison research is superior in another way. It measures school size in
terms of actual numbers, and with specific tipping points based on actual numbers. It
specifically assumes a linear [negative] relationship between school size and test scores.
In sharp contrast, prior research by Friedrich, Niccochea, et al. uses a logarithmic index
for school size. This assumes a non-linear relationship. Indeed, it assumes that the
number of students has declining effects, as schools get larger.
The Harrison research does not. It documents the fact that schools at all size
ranges are correlated with declining test scores. The relationship of school size with poor
student performance is monotonic over the entire range of schools.
Most importantly, tipping points are not as low as 100, 200, or 300 students, as
claimed by some prior researchers. Big schools of 1,000 or more, have especially low
scores, controlling for spending and class size, etc.
There is still another reason why the Harrison research is superior to the prior
research. They use different indices of socio-economic status for different schools or
districts. Moreover, they do not really control for poverty among students, but only the
occupation and education of their parents. Further, they do not control for racial
concentrations at all. The Harrison research does.
There is yet another defect with the prior research. It does not really measure
school size at all. It simply measures the number of students in a given grade. It fails to
concede that a school with a narrow grade range may have a lot of students in a given
year, but still enroll fewer students overall than other schools with a wider grade range.
The Harrison research measures school size in terms of all students within the school,
even when it selects out only schools with a majority of high school students.
Prior research also did not explicitly take into account possible effects on
academic outcomes due to the introduction of charter schools or special needs schools. It
simply lumps all schools or districts together. The Harrison methods exclude charter
schools or special needs schools, or explicitly control for the prevalence of special
education needs students.
Important results are found in New Jersey using the Harrison methods. A
significant linear negative correlation links school size with high school test scores, after
introducing statistical controls for spending (expenditures per student), student/teacher
(class-size) ratios, racial concentrations within the school, and student poverty (based on
students eligible either for free lunch or reduced price lunch subsidies). Even at the high
school level, school size profoundly hurts test scores, looking at lagged relationships
between school size and future test scores.
Russell Harrison - Report on School Size and Education Outcomes - Page 10
PRIOR RESEARCH ON OTHER ENDOGENOUS OUTCOMES:
CRIME, VIOLENCE, AND OTHER SCHOOL TRAITS THAT SIMULTANEOUSLY
CORRELATE WITH POOR TEST SCORES BOTH AS CAUSE AND EFFECT
Other prior research on school size goes beyond test scores and academic
achievement to look at other types of school behavior. The same historical pattern that
divides the empirical literature on academic behavior divides the literature on student
behavior. The qualitative advocacy research from the first half of the century usually
portrayed small schools, and especially small rural schools, in a demeaning manner.
Students in small schools in rural states were poorer than students in the big
schools of the urban Northeast. Students in the large schools in the urban, industrial
states generally were more prone to consider continuing on after elementary school to
higher levels, or after high school to higher levels. Students in the small rural schools
were more apt to leave schools early, not graduate from high school, and more often
report their desire to be farmers and homemakers, miners or beauticians, or other
professions that did not require college degrees.
Researchers from big city universities often treated the advocates of small town
schools as boobs and reactionaries, for wanting to hold on to community institutions
versus the greater resources available to large comprehensive, consolidated schools in
rich cities. Proponents of small schools were seen to represent the unenlightened legacy
of the agricultural era, versus the brave new world of the modern large-scale industrial
era.
Thus teachers, parents, administrators, and students in small school settings were
perceived as inferior to their counterparts in the big schools of the big cities. In response
to this logic, not only did consolidation proceed, but also thousands and millions of rural
and small town residents migrated to the wealthy industrial cities, which maintained their
competitive advantages up through the 1950s.
However, in the last half of the 20th century, the social and psychological benefits
of the small schools began to be recognized in new empirical research.13 Early in the
1960s Roger Barker and Paul Gump found that a much larger proportion of students in
small schools take part in after-school activities. In turn, other research found that
participation in extracurricular activities helped build self-esteem among students that
was correlated with superior academic performance, as well as less desire to dropout or
disrupt classroom decorum.
Subsequent research by Valerie Lee and her colleagues shows that the benefits of
small schools for students are matched by the benefits of small schools for teachers.14
13 Roger Barker and Paul Gump, Big School, Small School: High School Size and Student Behavior,
Stanford, California: Stanford University Press, 1964.
14 Valerie E. Lee and Julia B. Smith, ?Effects of High School Restructuring and Size on Early Gains in
Achievement and Engagement,? Sociology of Education, Volume 68, Issue 4 (October 1995), 241-270.
V. E. Lee, J. B. Smith, R. G. Croninger, 1995, ?Another Look at high school restructuring: More evidence
that it improves student achievement and more insight into why?, Issues in Restructuring Schools, No. 9,
Madison Wisconsin, University of Wisconsin Center on Organization and Restructuring Schools.
V. E. Lee and J. B. Smith, 1995, ?Collective Responsibility for Learning and its effects on gains in
achievement for early secondary school students?. Madison Wisconsin, University of Wisconsin, Center
on Organization and Restructuring of Schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 11
Teachers in small schools are far more apt to report feelings of self-esteem and
self-worth, in part due to better student behavior and achievement, and in part because
they become part of the informal decision-making process. Site-based decision-making
and other aspects of ?educational restructuring? become far more real in small schools,
even though larger schools and districts more often adopt symbolic ?innovations? and ?de
jure? reforms to deal with problems. Consensus, community, and communitarian virtues
help teachers succeed in small schools. In large schools teachers suffer from their
absence ? and from other key endogenous traits of a ?good school climate? or a
functional school ?culture?.
Still more recent research - funded by the U.S. Department of Education, the
National Institutes of Health, and the CDC ? has linked school size to adolescent health
risk behaviors, both in and out of school. This research provides extensive evidence of
the social, psychological, and public health benefits of small schools. Students in small
schools report much higher levels of ?connectedness? and ?trust? than students in large
schools. In turn the degree of ?connectedness? and ?trust? in the school is correlated with
favorable student behavior, and lower levels of student risk behavior including sexual
promiscuity, drug abuse, and delinquent behavior.
In studies of Chicago elementary schools, The Consortium on Chicago School
Research found a wide range of favorable school climate traits in elementary schools
with fewer than 350 students. These traits included:
?School leadership,
?Parental involvement,
?Teacher collegiality,
?Positive school-community relations,
?Trust among faculty members,
?Fewer incidents of adversarial politics.15
Nationwide surveys also confirm Chicago research that smaller schools have less
crime and violence. Nationwide, schools with less than 900 students have many fewer
incidents of school crime, and especially violent crimes, than larger schools. The schools
with more than 900 students have much worse rates of student crime, school violence,
and disruptive behavior so severe than police must be called.16
However, rarely does this research control for key exogenous variables that also
affect crime and violence in schools, besides school size. A great deal of delinquency
research and ?stress? theories emphasizes the importance of socio-economic variables
like race and poverty as determinants of delinquent behavior. A wide range of education
policy research stresses variables like class size and expenditures. However, most federal
data only aggregate nationwide surveys, and fail to provide cross-sectional breakdowns
amenable to regression analysis. They fail to measure the relationship of school size with
crime or violence outcomes controlling for race, poverty, class size, or spending. Thus
relationships are obscured.
15 See Wested Policy Brief, ?Are Small Schools Better? School Size considerations for Safety and
Learning?, San Francisco California, October 2001.
16 United States Department of Education, NCES, Digest of Education (Washington DC: various years).
Russell Harrison - Report on School Size and Education Outcomes - Page 12
The Need For New Research
In the 1999 legislative session, House Bill 168 (Session Law 1999-237; Section
8.33) directed the State Board of Education (SBE) to study the relationship between
school size and the behavior of students in North Carolina, as well as their academic
performance. The Evaluation Section?s Division of Accountability Services formed a
small team composed of in-house staff to study the issue, rather than employ independent
outside staff. The assignment was to review and summarize the available research on
school size, determine what statewide data were available to address the issue, and
provide a preliminary analysis of results.
After reviewing studies linking school size to non-academic outcomes, they
concluded that:
Previous studies of student behavior indicate that smaller schools are associated
with more positive outcomes for students. Larger schools are reported to have
higher dropout and expulsion rates than smaller schools. Larger schools also have
been shown to have more problems with most major behavioral issues including
truancy, disorderliness, physical conflicts among students, robbery, vandalism,
alcohol use, drug use, sale of drugs on school grounds, tobacco use, trespassing,
verbal abuse of teachers, teacher absenteeism, and gangs
However, they did not report whether these results were statistically significant. Indeed,
very little research has studied relationships between school size and these problems for
specific states, using cross-sectional data.
Next they analyzed data they had obtained for North Carolina. They concluded
that
Analyses of EOG and EOC data examined absolute performance as well as
achievement gains as a function of school size. Results indicated that smaller
elementary and middle schools tended to demonstrate higher achievement than
their larger counterparts, even after controlling for various student background
characteristics. These differences were small, however, typically amounting to a 1
to 2 scale score point difference. At the high school level, no achievement
differences were found between schools of varying sizes. Analyses of school
violence data and dropout rate in relation to school size did not yield any
significant associations, with one exception. Rates of violence in middle schools
appeared to increase slightly in larger schools after controlling for the poverty
level of students in the school. As was true for the achievement analyses,
however, this relationship was weak.17
In short, again prior research does not make it clear that school size may be
associated with problems of anomie and alienation for high school students as well as
younger students.
Thus the Harrison report for the New Jersey Commission on Business Efficiency
in the Public Schools is critical. It documents a quite different picture for New Jersey.
For years reforms have included various zero-tolerance policies, police in schools, and
new reporting requirements. A wide range of experimental programs has been launched
17 State Board of Education, Department of Public Instruction, Office of Instructional and Accountability
Services, Division of Accountability Services, Evaluation Section, ?School Size and its Relationship to
Achievement and Behavior?, April 2000.
Russell Harrison - Report on School Size and Education Outcomes - Page 13
to deal with school crime, student violence, and juvenile delinquency. Special funding
has been provided for high-risk districts. The state has dramatically intervened in certain
districts.
Nevertheless problems persist, especially in certain areas. Where and why?
One explanation is school size. As dependent variables the Harrison research
measures the degree to which student crime and school violence becomes isolated and
concentrated in one specific locality versus those in the surrounding county.
The results are significant. Namely, the correlations of school size (and district
size) with crime and violence are highly significant ? even looking specifically at high
school students. Big schools mean worse problems of anomie and alienation, based on
school self-reports. Where the average size of district schools is large, so is the
concentration of crimes and violence in that district ? all things else equal.
Why the New Research Design is superior to prior estimates
This new study uses a sophisticated research design that explicitly separates
exogenous and endogenous variables. Then it measures the lagged multiplier effects of
school size, independently of class size, spending per student, race, and socio-economic
status. School size is measured in the past, and crime and violence variables are
measured in the future.
In turn, it measures school size separately from district size. Independently of
how many schools are housed with a district, the district suffers from a concentration of
crime and violence within its schools as a linear function of average school size.
In turn, this is the same pattern found by the author in prior studies linking school
size with the isolation and concentration of poverty within specific schools or districts.18
Where schools are large, problems are concentrated, including problems of crime
and violence among high school students.
18 Russell Harrison, The Forum Newsletter, Spring 2001.
Russell Harrison - Report on School Size and Education Outcomes - Page 14
PRIOR RESEARCH ON INEFFICIENCY AND LOSS OF PRODUCTIVITY
Previous studies of ?polycentricity? show that smaller police districts produce a
variety of benefits to citizens. Namely, they tend to maximize citizen satisfaction and
trust with the providers, and minimize costs relative to what is accomplished. In contrast,
Leviathan police districts are less efficient, in that they spend a lot of money, but
problems of crime, disorder, fear, and mistrust remain.19 Community breaks down,
consensus declines, and the co-production of services is less effective. When one
measures outcomes in terms of multiple indicators, large-scale service delivery units are
not more efficient, but often less productive.
Other research on schools shows similar patterns. There is little or no evidence
that the size of schools reduces educational costs, or current spending per student, if one
takes into account certain possibilities:
?Small schools are mandated to incur costs due to standardized
administrative mandates that nominally apply to all schools, but especially
escalate costs for small schools. Every school must have a similar
minimum level of support staff. These cannot be shared among other
small schools. Every school must have certain facilities, which cannot be
shared with other governmental bodies or non-profit groups, much less
businesses. Thus very small schools are saddled with disproportionate
costs due to administrative rigidities. .
?Large schools escalate costs of land and transportation, and reduce the
possibility of using less expensive options to new construction of multiacre
stand-alone facilities.
?Large schools contribute to urban sprawl and the loss of potential multiacre
sites for green acre conservation, and reduce the conservation and
recycling of older facilities.
?Large schools, or at least large consolidated districts that house
consolidated schools, are associated with lower house values, as estimated
from ?hedonic price indices?. District consolidation causes a loss of local
control and a rise in political conflict. This hurts the socio-economic
resources of a community and reduces its taxable wealth.
?Large schools are correlated with school segregation produced by the loss
of middle class families and the concentration and isolation of poverty
students in the formerly large schools.
?Large schools produce severe social costs due to their disproportionate
levels of crime, conflict, anomie, alienation, absenteeism, and dropouts.
Nationwide, big schools are especially linked to dropouts.20 In turn the
concentration of dropouts produces disproportionate societal costs in terms of arrests,
police and court intervention, incarceration, babies born out of wedlock, improper care
and maltreatment of children, broken homes, and higher levels of infant mortality rates.
All these variables are closely linked among the states and metropolitan areas nationwide.
Large schools are highly inefficient, if one looks not just at money that is spent on
students who remain in schools, but take into account those students who are absent or
19 Michael McGinnis, editor, Polycentricity and local public economics (Ann Arbor, University of
Michigan Press, 1999. See chapters 1, 5, 7, 16, 17 in particular.
20 See L. Stefel et al, 1998. ?The Effects of Size of student body on school costs and performance in New
York City high schools. New York: New York University Institute for Education and Social Policy.
Russell Harrison - Report on School Size and Education Outcomes - Page 15
drop out due to deficient learning, which in turn produces a loss of self-esteem,
interpersonal conflicts, physical conflicts, and other juvenile health risk syndromes.
The Need for New Research
Unfortunately, prior research rarely looks at the lagged relationships of school
size with the compounded problems of educational inefficiency, even less for New
Jersey, and even less for high schools in particular.
Fortunately, new research has been undertaken. School inefficiency for New
Jersey has been measured by a composite index that measures standardized z-scores for
spending per student, (low) test scores on math, science, and reading separately, and
(high) scores for dropouts and absenteeism.
According to the ?polycentricity? theory, multiple traits should be used to
measure efficiency.21 In turn, inefficiency is maximized where school districts spend a
lot of money, to little or no avail, in their pursuit of improved test scores or improved
participation in the life of the school by students. Further, inefficiency is especially
severe when one measures the compounded problems for high schools where
absenteeism and dropouts are more severe than for primary schools.
What happens when one measures the relationship of school size with this
composite index of compounded inefficiency?
In New Jersey the linear relationships of school size with inefficiency are highly
significant. They persist even after controlling for various combinations of race, poverty,
special education students, class size, teacher training, computer resources and Internet
access.
Taking into account other explanations for educational inefficiency, school size
has a significant independent, autonomous influence.
In high school, big schools mean big problems that contradict national educational
goals, and frustrate New Jersey citizens eager for efficiency in the public schools.
21 Idem.
Russell Harrison - Report on School Size and Education Outcomes - Page 16
SUMMARY OF RESEARCH FINDINGS
Nationwide, prior research often shows school size to correlate with a wide range
of endogenous variables for students in primary and middle schools. However, the
evidence has been mixed for high schools, given the primitive research methods used in
prior studies.
In New Jersey the situation is now quite different. School size does make a
difference for high school students, using improved methods of measurement and
analysis.
The answer is emphatically yes to the following three questions:
(1) Is there a significant relationship linking school size with academic test
scores?
(2) Is there a significant relationship linking school size with the concentration of
school crime and student violence in a given district?
(3) Is there a significant relationship linking school size with an index of
inefficiency that measures the combination of high costs with low test scores,
plus unsolved problems of absenteeism and dropouts?
In every case, the ?ceteris paribus? relationships are significant at the .05 levels of
probability. This is true even for unweighted samples restricted only to schools and high
school districts serving grade 9-12 students. Weighted by the number of students in each
school or district, the relationships are often significant at the .001 level of probability.
Russell Harrison - Report on School Size and Education Outcomes - Page 17
DETAILED PROOFS AND EXPLANATIONS
In the next sections, I provide detailed proofs and explanations for each of these
conclusions. Sections where the results seem self-evident serve in effect as Appendixes
to the prior text. For other sections where the material is less obvious, more verbal text is
provided.
Sections 1 and 2 link school size with test score failures and school violence. They
show significant mean differences in problems facing large and small schools, and show
that these problems are highly significant when measured ?ceteris paribus?. The bigger
the schools, the bigger the problems. Each section provides a formal analysis of variance
to document significant differences in outcomes among different size schools, a graph to
visualize that larger schools have larger problems, and a multiple regression analysis to
measure relationships with school size controlling for other exogenous predictors like
poverty, race, class size, or teacher traits. Looking at schools where the social costs of
academic failure and school violence are especially severe, school size maximizes
adverse outcomes, controlling for other factors that might obscure the relationships.
In sections 3 and 4 I link school size with different indices of educational ?costs?. I
show that school size is significantly correlated with the more refined indexes of school
costs. These indexes (a) measure value added over time, (b) go beyond fiscal costs to
include academic costs like academic failure, plus (c) take into account social costs like
dropouts and absenteeism. Such indicators produce particularly clear results when
applied to a consistent set of schools, like mainstream high schools that consistently
report outcome data. Small size does not guarantee low costs, when one examines
?other? schools serving mostly ungraded or special needs students subject to special
federal and state mandates.
In Section 3, table 3a3 shows that over time a school size of 500-999 students is
associated with significant total cost savings per students versus schools housing 1,000-
1499 students. The mean savings in total costs of housing students start with $94.95 per
student in year one. They rise to $269.69 by year four. The median savings in total costs
of housing students start with $217.00 per student in year one. They rise to $422.00 in
year four.
The same table also shows savings versus schools of 1,500 or more students. The
mean savings in the total costs of housing students start with $296.03 per student in year
one. They rise to $337.80 by year four. The median savings in the total costs of housing
students start with $122.00 per student in year. They rise to $796.00 per student by year
four.
Comparing four different categories of school size, the differences of schools
housing 500-999 students versus other size categories are statistically significant at the
.001 level of probability for each of the four years analyzed.
Subsequent tables show even more significant cost savings when attention is paid
not just to the costs of housing students, but also to the costs of educating students. Even
higher levels of significance are achieved when one does not simply take into account the
number of schools within each size category, but also takes into account the total number
of students enrolled in each school in each size category.
Table 3a4 for example shows that the ratio of what it costs to what children learn
grows significantly in larger schools, comparing four size categories, weighting each
school by enrollment. Subsequent tables confirm the same pattern.
Russell Harrison - Report on School Size and Education Outcomes - Page 18
Part A of Section 3 explains differences in how to measure the costs of housing
students versus the costs of educating students. Part B of Section 3 explores in greater
detail the relative merits of schools in the size range of 500-999 students. Part C of
Section 3 explores in greater detail the relative costs of schools housing 1500 or more
students.
This research was not asked to identify the optimal size of schools. Different
schools may weight different roles in different ways. However, New Jersey schools that
house 500-999 students show major advantages both in their custodial role and in their
role of educating students.
Section 4 shows that the results are most emphatic when analysis takes into
account the full range of academic and social costs produced by larger schools. These
include social costs like dropouts and absenteeism, plus academic costs like failures on
HSPT tests of math, reading, and writing. Looking at different indices of ?compounded?
inefficiency and ?residual? inefficiency that adjust for the poverty, racial composition,
class size, and other traits of each school, school size is strongly correlated with a wide
constellation of inefficiency costs that must be borne by New Jersey tax payers.
Overall the evidence makes clear that the custodial costs of ?housing? students are
not as systematically related to school size as are the training costs of ?educating?
students. Educational Policy Makers and the public should insist that future research take
into account the total costs of school.
For example, many large schools reduce their ?custodial? costs of ?housing?
students by encouraging absenteeism on any given day, plus dropouts over time, to
exclude the marginal student who is hardest to house or educate.
Many other large schools use other strategies as well to control nominal costs. In
the short run they crowd more students into a given 1,000 square feet of floor area. This
cuts nominal costs. However, by the end of a four year cycle they may have far fewer
students per floor area, due to excessive attrition. This makes it harder to achieve a high
graduation rate, unless they simply ignore the number of 9th grade students who should
have made it to grade 12, but did not.
Thus it is important to measure the effects of school size over time, and not just
short-term cost/ benefit ratios. Over time the ratio of costs to benefits grows, as a
function of school size, especially if one compares comparable schools that exclude small
?other schools? facing inflated costs due to ?special need? mandates.
Sections 5 and 6 summarize the methodology used in sections 1-4. They explain
data sources, how many schools were analyzed, key indicators used in this research, and
the vocabulary common to hypothesis testing and regression analysis ? which is generally
not very common at all outside the research community.
Sections 7 and 8 outline relevant readings for issues in debate. Many older
studies strongly insisted that big schools and big districts have big virtues. Of course,
they often reached this conclusion by confusing the resources available within a school to
the realization of desired outcomes. Even among the schools studied by Conant and
other proponents of big schools, a reanalysis of their purported evidence shows adverse
correlations between school size and desired outcomes.
Russell Harrison - Report on School Size and Education Outcomes - Page 19
Based on their own evidence:
?School size was negatively correlated with: the proportion of students able to
meet basic standards favored by Conant.
?School size was negatively correlated with the proportion of students who
participated in programs for the gifted and talented also favored by Conant.
?School size was negatively correlated with a school climate that was safe and
secure, and positively correlated with a school climate marked by chaos and
confusion.
More recent studies point out growing evidence of better outcomes from the small
school learning community. They also clarify research methods and theoretical
perspectives to quantify and explain those outcomes.
Section 9 outlines a range of policy options to implement these findings, while
Section 10 advocates further research to clarify the case for the small school learning
community in New Jersey and beyond. They outline a wide range of issues to be
explored in future research. However, based on feedback from Commission members
and others, the following issues deserve special consideration in follow-up studies:
o What is the relationship of school size to problems affecting middle school
and junior high school students in particular, including failures on GEPA
tests, school crime and violence, and a poor school climate overall?
o What is the relationship of school size to problems affecting grammar school
students in particular, including low ESPA scores, absenteeism, and limited
family involvement in the life of the school?
o What is the relationship of school size with student crime and violence, using
unpublished data not yet available to the public?
o In explaining differences in school crime and violence, how superior are
?gemienschaft? reform methods based on small school learning communities
versus ?gesellschaft? methods. The latter authoritarian methods seek to
replace informal social controls with formal controls like zero tolerance
regulations, automatic reporting of student crimes to police, police in schools,
metal detectors, DARE style intervention programs. To what degree is the
small school learning community strategy superior? To answer such
questions, research should utilize methods and theoretical perspectives like
those outlined at the 2003 International Conference on Violence and Family
Maltreatment held in San Diego California, sponsored by the Chadwick
Center and the San Diego Children?s Hospital, and especially the CEU
workshop on school violence.
o What are the potential outcomes (including savings in fiscal costs and benefits
for social and academic goals) from a balanced shift between class size and
school size reduction policies? To what extent would such a shift meet goals
including cost savings of several hundred million dollars a year, while
improving academic performance, reducing fear among students and teachers
from school conflict and crime, plus minimizing dropouts, absenteeism, and
violence? To obtain such results, use might be made of the computer
simulation methods outlined at the 2002 School Conference on School Crime
and Violence sponsored by the Rutgers University Forum for Policy Research
and the Medical School of Osteopathic Medicine at Stratford, before a panel
headed by Assemblywoman Mary Previte. Multivariate regression analysis
Russell Harrison - Report on School Size and Education Outcomes - Page 20
methods like those used in ?institutional? research should explore whether
small class size policies are increasingly inefficient within New Jersey,
compared to small school policies, as predicted by Erik Hanushek and others.
Russell Harrison - Report on School Size and Education Outcomes - Page 21
SUMMARY OF DETAILED PROOFS AND EXPLANATIONS
I Four sections summarize the statistical evidence that school size is significantly linked
to adverse educational outcomes for New Jersey High Schools, so that the null hypothesis
can be and should be rejected for each type of outcome:
?Section 1 links School Size with future Test Score Failures.
?Section 2 links School Size with future School Violence.
?Section 3 shows different ways that School Size links with indicators of housing
costs versus educational costs: The Custodial School House Function versus the
Educational Value Added Function.
?Section 4 links School Size with ?value added? indices that measure educational
costs, including indexes of ?compounded? inefficiency and ?residual?
inefficiency ? both of which are significantly exacerbated by larger schools.
II Two sections outline and review the Research Methodology to explain how the
present results were obtained, and to serve as a guide for future research
?Section 5 explains where to find the evidence.
?A. Data Sources.
?B. Criteria for Selection of 100% Comprehensive Samples.
?C. The Number of Cases in Each Universe of Cases/ Sample Size.
?Section 6 summarizes and explains the statistical data and concepts.
?A. Key Variables Used In This Research.
?B. Key Concepts Used In Regression Analysis And Hypothesis Testing.
III. Two sections inventory background readings that clarify what is known about school
size outcomes, how they should be measured, and major implementation issues regarding
incremental approaches to the small school learning community.
?Section 7 focuses on optimal research methodologies.
?Section 8 points to substantive research on School Size Outcomes and
Implementation Options.
IV. Two sections outline the range of Research Priorities and Follow-up Efforts available
to the New Jersey Commission on Business Efficiency in the Public Schools, and other
advocates of change and improvement in how well public schools operate.
?Section 9 clarifies the range of policy options the Commission should consider for
implementing a Small School Learning Community.
?Section 10 emphasizes the need for follow-up studies sponsored by the
Commission. New evidence is needed to build a comprehensive needsassessment,
environmental-scanning, and strategic planning process to cut costs
and expand favorable educational outcomes for public schools in New Jersey.
Russell Harrison - Report on School Size and Education Outcomes - Page 22
SECTION 1 ? SCHOOL SIZE AND ACHIEVEMENT
The tables in section 1 provide statistical evidence that school size is significantly
linked to the percent of high school students who pass or fail key HSPT tests. School
size is negatively linked to the percent of students who pass. This means that school size
is positively linked to the percent who fail those tests. The negative relationship between
school size in the past and HSPT test scores in the future are consistent enough to reject a
null hypothesis that the relationship of school size with test proficiencies is random.
Various tables cover the following topics:
1.1: Looking at Bivariate Relationships, The Differences in High School Proficiency
Test Scores between Schools of Different Size are Sufficient to Reject Null
Hypotheses for Math, Reading, and Writing
Table 1.1: Students in small high schools in New Jersey performance
significantly better than students in large high schools, comparing mean
scores on High School Proficiency Tests for high schools above and below
1,500 students
1.2: Looking at simple graphs, one sees a clear picture of major differences in test
scores among different size categories of schools, using 500, 1000, and 1,500 students
as tipping points
Figure 1.2a:
Net Gaps between average math scores for each size category of
high schools versus State Mean for all High Schools: Larger
Schools have worse math scores in the future
Figure 1.2b
Net Gaps between average reading scores for each size category
of high schools versus State Mean for all High Schools: Larger
Schools have worse reading scores in the future
Figure 1.2c
Net Gaps between average writing scores for each size category of
high schools versus State Mean for all High Schools: Larger
Schools have worse writing scores in the future
1.3: Multiple Regression Coefficients document significant linkages over time
between school size and High School Proficiency Test Scores, after controlling for
Spending, Class Size, and other School Traits for Students and Teachers
Table 1.3
Multiple regression analysis coefficient show the linkage of school
size with proficiency test score results among NJ High Schools is
statistically significant, so that the null hypothesis can be rejected,
even after imposing various ?ceteris paribus? controls, plus
measuring ?lagged? multiplier effects over time, plus looking at
test scores individually (in different equations)
Russell Harrison - Report on School Size and Education Outcomes - Page 23
Table 1.1a: Students in small high schools in New Jersey perform significantly better than students in
large high schools: A comparison of mean (average) passing rates on High School Proficiency Tests
for high schools above and below 1,500 students
% Students Passing HSPT tests in 1999-2000, as a function of lagged school size in 1996-1997
School Size
In 96-97
Average % passing
In 1999-2000 by subject area
MATH READING WRITING
0-1499
Mean 93.69 91.87 93.25
Geometric Mean 93.03 91.00 92.68
N of schools 261
1500 and above
Mean 86.47 82.89 86.77
Geometric Mean 84.64 80.53 85.16
N of schools 48
All Schools
Mean 92.57 90.48 92.24
Geometric Mean 91.67 89.29 91.47
N of schools 309
ANOVA (Analysis of Variance: Impact of school size
on lagged test scores
F-coefficient (ANOVA) 18.27 22.51 17.16
Sig Coefficient 0.00003 0.00000 0.00004
Is the statistical significance of the relationship
between school size and lagged test scores
sufficient to reject the null hypothesis at the .05
and/or .01 level of probabilities?
yes, yes yes, yes yes, yes
Measures of the degree that smaller high schools
have better test scores than larger high schools,
reported as a % (percent) of the mean for all schools
[for a tipping point of 1500]
MATH READING WRITING
Mean 7.80 9.93 7.03
Geometric Mean 9.14 11.72 8.22
Russell Harrison - Report on School Size and Education Outcomes - Page 24
Table 1.1b
The Universe of Cases and Measurement Methods for Section 1
(Tables 1.1, 1.2, 1.3)
All data sources were analyzed using SPSS 11 to measure ?lagged relationships? over time. Thus
school size was measured several years prior to test results, using a ?lag? of three years to estimate
relationships over time.
High School Proficiency Test HSPT results were taken from NJ DOE ?Report Card Tables? for 1999-
2000.
Data for school size were taken from U.S. Department of Education, Common Core of Data CCD files,
1996-1997
The Universe of Cases includes 309 schools that meet several criteria. (a) The 1996-1997 US CCD
report classified them as ?high schools?. (b) The same source reported CCD enrollment data (for 1996-
1997). This criterion omitted certain charter and alternate schools created after 1996-1997 (c) The NJ
DOE ?Report Card? files reported HSPT data for 1999-2000.
The ?samples? used in Section 1 include 100 percent of the high schools that met all three criteria.
However, Table 1.3 includes only 300 schools, since nine schools failed to report complete data for all
variables in a multivariate regression analysis. However, the basic strategy is to report results for a
comprehensive, exhaustive, 100% sample of the universe of cases defined.
Table 1.1a divides the universe/sample of 309 high schools into two size categories. It compares 261
schools with 0-1499 students, versus 48 schools with 1,500 or more students, based on U.S.DOE CCD
enrollment totals reported for 1996-1997.
Figure 1.2a,b,c uses the same sample/universe of 309 high schools. However, it uses four size
categories. The results show the same monotonic decrease in the % who pass HSPT tests for larger
schools - when one compares schools in four size categories: 0 - 499, 500 ? 999, 1000-1499, as well
as 1500 and above. The total sample refers to the 309 schools with full data for 1996-1997 and 1999-
2000. There were 58, 139, 87, and 48 schools respectively in each size category.
Table 1.3 began with the same potential ?universe? of 309 schools. The sample was reduced to 300
schools. Nine schools were omitted since they lacked complete data for all the predictor variables
used in the regression equations.
It should be noted that similar results linking school size to the % of students passing the HSPT tests
were obtained using slightly different criteria to refine the sample, e.g., only schools with at least 100
students, or only schools with 10 or more students taking the tests, or only schools reported as regular
high schools both in 1996-1997 and 1999-2000.
Future research is needed to estimate results for GEPA tests for middle school students, and ESPA
scores for elementary students. This research was limited to high school students enrolled in high
schools operating in the period 1996-1997 through 1999-2000.
All the data used in this report are publicly available from the
U.S. DOE and the N.J. DOE
to facilitate public review.
Field name used by NJ Report Card to report HSPT
scores for individual schools, supplied by the NJ
Department of Education (where y6 = 1999-2000)
math_y6 read_y6 write_y6
SPSS field name HSPT030 HSPT029 HSPT031
Russell Harrison - Report on School Size and Education Outcomes - Page 25
Figure 1.2a:
Net Gaps Between Average % Passing HSPT Math Tests
for each Size Category of High School
versus State Mean for all High Schools in sample:
Larger Schools have worse math scores in the future
(1999-2000 versus 1996-1997)
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
School Size Categories:
Lagged number of Students 3 years prior to tests
Mean HSPT score for Size category minus Statewide Average
Net Gaps Between Average
Math Scores versus State mean
for all schools
3.41 1.79 -0.87 -6.10
0 - 500 students
500 - 1000
students
1,000 - 1,500 1,500 and above
Russell Harrison - Report on School Size and Education Outcomes - Page 26
Figure 1.2b:
Net Gaps Between Average % Passing HSPT Reading Tests for
Each Size Category of High Schools
versus State Mean for all High Schools in sample -
Larger schools have worse reading scores in the future
(1999-2000 versus 1996-1997)
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
School Size Category:
Lagged Number of Students 3 years Prior to Tests
Mean HSPT Score for Size Cateory minus Statewide Average
Net Gaps Between Average
Reading Scores versus State
mean for all schools
4.81 -0.08 -3.05 -9.68
0 - 500
students
500 - 1000
students
1,000 - 1,500
1,500 and
above
Russell Harrison - Report on School Size and Education Outcomes - Page 27
Figure 1.2c
Net Gaps Between Average % Passing HSPT Writing Tests for each Size
Category
of High Schools versus State Mean for all High Schools in sample -
Larger schools (1996-97) have worse writing scores in the future (1999-00)
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
School Size Category:
Lagged Number of Students 3 years prior to tests
Average HSPT Scoe for Size Category Minus Statewide Average
Net Gaps Between Average
Writing Scores for each Size
Category of High Schools
versus State mean for all
High Schools
3.30 1.37 -1.35 -5.80
0 - 500
students
500 - 1000
students
1,000 - 1,500
1,500 and
above
Russell Harrison - Report on School Size and Education Outcomes - Page 28
Table 1.3: Multiple Regression Analysis Coefficients Show the Linkage of School Size with Proficiency Test Score
results among NJ High Schools is Statistically Significant, so that the null hypothesis can be rejected, even after
imposing various "ceteris paribus" controls, plus measuring "lagged" multiplier effects over time, plus looking at test
scores individually
Dependent Variable = HSPT (test) scores for 300 NJ High Schools with complete data Math Reading Math Writing
Total predictors = Number of control variables + school size 8 9 9 9
Equation Type (1 or 2): Both equations include school size plus other predictors that
control for spending, federal aid, class size, student/faculty ratios, teacher education (%
undergraduate degrees only), mobility (turnover) rates for students. Equation 1 controls
for percent black. Equation 2 controls for percent minority, plus ungraded students.
Other equations give similar results, using data provided by the U.S. and N.J.
Departments of Education.
The sample of 300 schools excludes nine high schools lacking full data for all predictor
variables.
1 2 2 2
MRA Coefficient How derived Math Reading Math Writing
R-square Coefficient for all
predictor variables proportion of variation in DV explained by all predictors 0.694 0.677 0.625 0.591
F Coefficient for overall
equation
ANOVA coefficient 82.411 67.484 53.729 46.491
Sig Coefficient for overall
equation
Statistical Significance for entire equation (probability of
error in rejecting the null hypothesis) 0.000 0.000 0.000 0.000
Unstandardized Coefficient for
School Size "Ceteris Paribus" Slope (B coefficient) -0.0039 -0.0027 -0.0028 -0.0022
Average Reduction in % of students tested who pass the HSPT, as a function of each
extra 1,000 students in school -3.865 -2.676 -2.836 -2.242
Average reduction in previous passing rate as a % of the range in scores for all schools
in sample -6.155 -3.890 -4.516 -3.570
Beta Standardized Regression Coefficient using z scores for
all variables (standard deviation units) -0.178 -0.109 -0.130 -0.112
Average % decrease in test scores over 3 year period, for each increment in school
size of one standard unit, measuring test scores in standard units (z scores) as well -17.769 -10.906 -13.037 -11.167
t coefficient Ratio of slope to standard error -4.917 -2.857 -3.171 -2.599
Sig Coefficient for School
Size-Test Score Relationship,
"all things else equal"
Probability of error in rejecting the null hypothesis that
no relationship exists between school size and
proficiency test scores, after eliminating effects on
relationship due to other control variables or "ceteris
paribus" conditions
0.000 0.005 0.002 0.0098
Is the statistical significance of the relationship linking school size with
HSPT scores sufficient to reject the null hypothesis, either at the .05
and/or .01 levels of probability (i.e., at the 95% and/or 99% confidence
levels, for the sample of 300 high schools operating between 1996-
1997 and 1999-2000)?
yes, yes yes, yes yes, yes yes, yes
Russell Harrison - Report on School Size and Education Outcomes - Page 29
SECTION 2 - SCHOOL SIZE AND VIOLENCE
The tables in section 2 provide statistical evidence that school size is significantly
linked to test school violence at a level sufficient to reject a null hypothesis about the
relationship of school size with school violence. Looking at types of students and
districts where the problems of violence are especially serious, dramatic evidence links
school size with the concentration of violence in a district.
2.1: Looking at Bivariate Relationships, the Differences in Violence Indices between
Districts with Different Size Schools are Sufficient to Reject Null Hypotheses about
Size-Violence Relationships
Table 2.1: Linkages Between school size and lagged indices of school
violence for 51 New Jersey (regional) high school districts:
?Four different indexes show that the future concentration of
violence in high school districts ranges from 86 to 148% higher where
schools are larger (above 1000 average enrollment)
?High school districts with larger schools have significantly more
violent incidents among students versus other nearby school districts
within the county.
2.2: Simple graphs give a clear picture of the extent of differences in violence indices
between districts with large and small schools. The percent differences or variances
of violence indices from the average for all districts in the sample are compared for
large and school schools. High School Districts with large schools have much higher
levels of violence relative to the average for all high school districts studied.
Figure 2.2a:
How the Mean Violence index 1 compares to the statewide average
? contrasting high school districts with large and small schools
(using 1,000 students as a tipping point):
Large Schools in the past are characterized by the geographical
concentration of violence over time using index 1
Figure 2.2b
How the Mean Violence index 1 compares to the statewide average
? contrasting high school districts with large and small schools
(using 1,000 students as a tipping point):
Large Schools in the past are characterized by the geographical
concentration of violence over time using index 2
Figure 2.2c:
How the Mean Violence index 1 compares to the statewide average
? contrasting high school districts with large and small schools
(using 1,000 students as a tipping point):
Large Schools in the past are characterized by the geographical
concentration of violence over time using index 3
Russell Harrison - Report on School Size and Education Outcomes - Page 30
Figure 2.2d
How the Mean Violence index 1 compares to the statewide average
? contrasting high school districts with large and small schools
(using 1,000 students as a tipping point):
Large Schools in the past are characterized by the geographical
concentration of violence over time using index 4
2.3: Multiple Regression Coefficients document significant linkages over time
between school size and High School Violence, after controlling for Spending, Class
Size, and other School Traits for Students and Teachers
Table 2.3
Multiple regression analysis coefficient show the linkage of school
size with violence among NJ High Schools is statistically
significant, so that the null hypothesis can be rejected, even after
imposing various ?ceteris paribus? controls, plus measuring
?lagged? multiplier effects over time
Russell Harrison - Report on School Size and Education Outcomes - Page 31
Table 2.1a: Linkages between School Size in 1996-1997 and Lagged Indices of School Violence during 1999-2000
For 51 NJ High School Districts
Four Different Indexes Show that the Future Concentration of Violence in High School Districts Ranges from 86 to 148% higher where schools
are larger (above 1000 average enrollment)
High School Districts with Larger Schools have significantly more Violent Incidents Among Students versus Other Nearby School Districts
within the County. [School size is based on 1996-1997 enrollments and the degree of school district violence is based on 1999-2000 incidents.]
The Universe/ Sample of cases includes 51 NJ School Districts that serve predominantly High School Students. Over 50% of all students
enrolled in grades 9-12 during 1996-1997, while the NJ DOE included the district in its crime and violence reports for 1999-2000. The universe/
sample includes districts located in 15 counties, including all major ?regional? high schools and a couple of ?service commission? schools. The
percent of high school students ranges from 51 to 100 percent.
Using data weighted by enrollment, the relationships are highly significant between enrollment in 1996-1997 and violence indices for 1999-
2000. Even with the un-weighted sample of 51 cases, the evidence rejects the Null Hypothesis at the .05 confidence limit, regarding linkages
between School Size and the Geographical [spatial] Concentration of Violence within Individual High School Districts.
Some of the key Indicators follow:
Concentration of Violence Indices:
The proportion of total violence
within each county that occurs
within a specific district (%)
The ratio of Violent Incidents within
Each District versus Other Districts in
the County {%}
Comparing Differences In Means for ANOVA
Average Size for District Schools in 96-97
Mean Violence Index 1 Mean Violence Index 2
Mean School size of 0-999 (n = 34) 3.56 3.94
Mean School size of 1000 and above (n=17) 7.89 9.54
Total Districts in sample (n=51) 5.01 5.80
ANOVA F coefficient for mean differences in
violence index among only those 51 NJ Districts
with a Majority High School Level Students
6.198 5.388
Sig Coefficient for these 51 NJ HS Districts 0.016 0.024
Can the null hypothesis be rejected at the .05 level
of probability for a sample this small? YES YES
Validity Checks
Comparing Violence in Median Districts
Size Category for High School District
Median Violence Index 3 Median Violence Index 4
Mean School size of 0-999 (n=34) 1.82 1.86
Mean School size of 1000 and above (n=17) 6.09 6.49
Total Districts in sample (n=51) 3.01 3.11
Russell Harrison - Report on School Size and Education Outcomes - Page 32
Table 2.1b
Comparing the Range of Violence Indices between High School Districts with Large versus Small Schools
(Using 1,000 as a tipping point)
Mean Violence
Index 1 as a % of
Statewide Average
Size Category for High School District Mean Violence Index 2 as a
% of Statewide Average
Mean school size of 0-
999 (n=34) -28.83
Mean school size of 0-999:
To what extent does the mean violence index vary
from the average for all 51 districts in the sample?
-32.20
Mean school size of
1000 and above (n=17) 57.65 Mean school size of 1000 and above
64.39
Median Violence
Index 3 as a % of
Statewide Average
Size Category for High School District Median Violence Index 4 as a
% of Statewide Average
Mean school size of 0-
999 (n=34) -39.52 Mean school size of 0-999 -40.25
Mean school size of
1000 and above (n=17) 102.07 Mean school size of 1000 and above 108.69
Each Range measures the degree that Districts with larger schools have a worse concentration of violence than Districts with
smaller schools, measured as a percent of the State Average for All 51 High School Districts.
Russell Harrison - Report on School Size and Education Outcomes - Page 33
Figure 2.2a: The % Difference or Variance in the Mean Violence Index 1
from the Statewide Average for 51 districts-
Comparing HS districts with large and small schools
(using 1,000 students as a tipping point)
-40.00
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Average School Size in District
Average Concentration of Violence -
Index 1 by School Size Category
Mean Violence Index 1 as a % of
Statewide Average - Comparing
HS districts with large and small
schools (using 1,000 as a tipping
point)
-28.83 57.65
Mean school size of 0-999
Mean school size of 1000 and
above
Russell Harrison - Report on School Size and Education Outcomes - Page 34
Figure 2.2b: The % Difference or Variance in the
Mean Violence Index 2 from the Statewide Average for 51 districts-
Comparing HS districts with large and small schools
(using 1,000 students as a tipping point)
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
Average School Size in District
Average Concentration of Violence -
Index 2 By School Size Category
Mean Violence Index 2 as a %
of Statewide Average -
Comparing HS districts with
large and small schools (using
1,000 as a tipping point)
-32.20 64.39
Mean school size of 0-999
Mean school size of 1000 and
above
Russell Harrison - Report on School Size and Education Outcomes - Page 35
Figure 2.2c: The % Difference or Variance in
the Median Violence Index 3 from Statewide Average for 51 districts-
Comparing HS Districts with Large and Small Schools
[using 1,000 students as a tipping point]
-60.00
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Average School Size in District
Average Concentration of Violence -
Index 3 by School Size Categories
Median Violence Index 3 as
a % of Statewide Average
-39.52 102.07
Mean school size of 0-999
Mean school size of 1000 and
above
Russell Harrison - Report on School Size and Education Outcomes - Page 36
Figure 2.2d
The % of Difference or Variance of the Violence Index
from the Statewide Average for 51 Districts
Median Violence Index 4 as a % of Statewide Average -
Comparing Districts with Large and Small Schools
[using 1,000 students as a tipping point]
- 6 0 . 0 0
- 4 0 . 0 0
- 2 0 . 0 0
0 . 0 0
2 0 . 0 0
4 0 . 0 0
6 0 . 0 0
8 0 . 0 0
1 0 0 . 0 0
1 2 0 . 0 0
Average School Size in District Average Concentration of Violence -
Index 4 by School Size Category
Median Violence
Index 4 as a % of
Statewide Average
-40.25 108.69
Mean school size of 0-
999
Mean school size of 1000
and above
Russell Harrison - Report on School Size and Education Outcomes - Page 37
Table 2.3a: Multiple Regression Analysis confirms a statistically significant relationship
between School Size in the past and the Geographical (Spatial) Concentration of Violence
Within A District in the future, even after controlling for district size, race/ethnicity, poverty,
spending, and class size.
Index 1 measures the % of all violent incidents within county schools that are
concentrated within a given district. [SHR_VIO]
Predictor Variables (sorted by
statistical significance)
Standardized
Regression
Coefficient: Beta
t-ratio of slope to
standard error
Sig. Coefficient
(probability of error
in rejecting the null
hypothesis)
Lagged School size: Mean of total
students per regular school during
1996-97 (from U.S. D.O.E. CCD files)
0.4288 2.4112 0.0208
District Size: 2001 Resident
Enrollment for District 0.1678 0.9170 0.3649
Race 2000: Per cent Asian students -0.1467 -0.7409 0.4633
Race 2000: Per cent white students 0.1709 0.7356 0.4665
Poverty: 2000 Per cent eligible for free
lunch or reduced price lunch 0.1300 0.4963 0.6225
Spending: 2001-02 Comparative Cost
Per Pupil 0.1509 0.4433 0.6600
Special Needs: 2001 Total Eligible for
Special Education % (pct) 0.0730 0.3510 0.7275
Intergovernmental: Local Taxes as
proportion of 01-02 Revenue Sources -0.0294 -0.1169 0.9075
Class size: 2001 Student/ Teacher
Ratio: 100 Students per Teacher Ratio
Fall 2001 (Certified Staff)
-0.0005 -0.0020 0.9984
Russell Harrison - Report on School Size and Education Outcomes - Page 38
Table 2.3b: Multiple Regression Analysis confirms a statistically significant relationship
between School Size in the past and the Geographical (Spatial) Concentration of Violence
Within A District in the future, even after controlling for district size, race/ethnicity, poverty,
spending, and class size.
Index 2 measures the Ratio of all violent incidents within
a given district versus all nearby districts within the county. [RTO_VIO]
Predictor Variables (sorted by
statistical significance)
Standardized
Regression
Coefficient: Beta
t-ratio of slope to
standard error
Sig. Coefficient
(probability of error
in rejecting the null
hypothesis)
Lagged School size: Mean of total
students per regular school during
1996-97 (from U.S. D.O.E. CCD files)
0.4892 2.7355 0.0094
Race 2000: Per cent white students 0.1671 0.7151 0.4789
Race 2000: Per cent Asian students -0.1369 -0.6877 0.4958
District Size: 2001 Resident
Enrollment for District 0.1042 0.5666 0.5743
Poverty: 2000 Per cent eligible for free
lunch or reduced price lunch 0.1294 0.4915 0.6259
Spending: 2001-02 Comparative Cost
Per Pupil 0.1134 0.3314 0.7421
Special Needs: 2001 Total Eligible for
Special Education % (pct) 0.0600 0.2870 0.7756
Intergovernmental: Local Taxes as
proportion of 01-02 Revenue Sources 0.0496 0.1958 0.8458
Class size: 2001 Student/ Teacher
Ratio: 100 Students per Teacher Ratio
Fall 2001 (Certified Staff)
-0.0123 -0.0536 0.9576
The sample includes only those 51 NJ districts with a majority of high school (grades 9-12)
students in 1996-1997, that were included in the survey of crime and violence for 1999-2000.
Even for a sample of only 51 cases, and with 8 control variables, the null hypothesis can be
rejected at a .05 level of probability regarding the relationship of school size and school
violence over time. The same conclusion holds for each index of school violence.
The control variables include district size, as well as class size, two measures of spending, two
measures of race, a composite index of student poverty, plus special needs enrollment.
All variables were measured using information provided by the U.S. and N.J. Departments of
Education.
Russell Harrison - Report on School Size and Education Outcomes - Page 39
SECTION 3 - SCHOOL SIZE AND COST
THE CUSTODIAL/ SCHOOL HOUSE FUNCTION VERSUS
THE VALUE ADDED/ EDUCATION FUNCTION
This section shows how School Size links with different indicators of ?Costs? in New
Jersey. The first set of indicators measure how efficiently or inefficiently schools provide
their custodial role, or ?The School House Function?. These indicators simply measure
how much it costs to house a given number of students during a given year. The more
sophisticated indicators measure how efficiently or inefficiently schools provide their
teaching mission, or ?The Educational Value Added Function?.
For the latter case of indicators, it seems important to look not just at short run costs,
but long run costs. It is important to measure how much it costs to educate students, not
just in providing short run floor space, but in improving how well they learn and flourish
in the long run. Doing so helps clarify how school size affects outcomes.
To understand the contrast between the custodial costs of housing students and the
training costs of educating students, it is important to understand the contrast between the
quantity of schooling and the quality of schooling. Both in the United States and other
countries, the goals of quality and ?value added? are assuming ever greater importance.
Reformers place growing attention on the need to measure and enhance the ?value
added? function of schools.
In the past, educational outcomes were measured simply in terms of how many
children attended classes, and the number of years of schooling they completed. Now
educational outcomes include how much children learn at any given level of schooling.
The public wants schools to educate children to meet high standards of learning, and not
just keep them off the streets for a given number of hours, days, and years. Outcomes
imply proficiencies, and not just how many students are enrolled.
Of course, many working parents also demand an expanded custodial function for
schools. Many want school boards to expand the school day and school year, by starting
earlier and ending later. Such changes can greatly expand the costs of the housing
function. Thus government must balance demands for an improved quality of schooling
with demands for an improved quantity of schooling. Officials need to identify structures
than can maximize goals of quality and quantity in a cost efficient manner.
In any event, expanding demands placed on local school boards and state officials can
alter both the housing function and the education function, and make the task of
maximizing efficiency even more important.
This initial look at school costs in New Jersey does not necessarily produce a simple
answer to where costs are greatest, for those who fail to see the need to differentiate the
different functions provided by schools The present research does reveal an important
result for those interested in more subtle nuances.
Namely, for New Jersey, the relationship of school size is more consistently
correlated with the quality of education versus the quantity of schooling. This is
especially true when one looks at more sophisticated indices of quality or value added
over time. It is much harder to predict which size schools will have the lowest costs for
housing children as part of their custodial role. It is much easier to predict and prove
which size schools do the best job of educating children.
Russell Harrison - Report on School Size and Education Outcomes - Page 40
Certain types of cost indicators particularly blur the task of understanding causes for
custodial costs. These crude indices simply divide aggregate spending by na?e quantity
indices. They simply add up nominal enrollments and projected class rosters at the
beginning of a school year. Such indices ignore how many children attend class over
time, and actually graduate with their cohort. They miss an important point. Namely,
school size affects patterns of dropouts and attendance.
Larger schools produce adverse conditions that exaggerate dropouts and absenteeism.
Big schools produce a complex set of social, academic, and fiscal costs that plague
students and parents, and those concerned with the costs of educating students. However,
by eliminating marginal students over time, they reduce their nominal costs of housing
students. Larger schools also tend to house a larger number of students per 1,000 square
feet. Again, this is one of the ways they reduce their nominal costs of housing students.
By holding down the costs of housing students, they make it harder to achieve their
responsibility to educate students.
The next two sections clarify differences in the housing and educating roles of
schools. Namely, Section 4 will explore educational quality issues or value added issues,
to show how large schools reduce benefit/ cost ratios. Section 3 will focus more closely
on the quantity issue, or the custodial costs of housing students. It will outline different
ways to measure costs, and how different cost indices vary as a function of school size in
New Jersey.
Part A explains and illustrates differences between indices that measure the costs of
housing students versus the costs of educating students. It shows that the costs of
educating students are consistently higher in larger schools. Larger schools spend
significantly more compared to what students learn. Size is closely linked to the ratio of
benefits learning to fiscal costs.
In contrast, less sophisticated indices for housing costs do not follow a consistent
pattern in regard to school size, especially in terms of short-term costs. In particular,
costs are often quite high in very small schools required to must provide specialized
services and facilities for ungraded students in ?other? schools.
On the other hand, certain charter schools spend relatively little compared to other
schools in their county or municipality, since they are only funded at about 90 per cent of
other schools, and often lack permanent facilities. As more charter schools are created,
their expansion may reduce the apparent costs per pupil in small schools, since charter
schools tend to be very small.
In short, because the mission of schools varies, so do their costs of housing students.
Thus school size does not follow a consistent pattern with the costs of ?housing?
students, at least at first glance. However, one finding is important. Namely, New Jersey
schools with 500-999 students may have extremely favorable cost ratios for housing
students.
Part B focuses more extensively on cost differences between schools with 500-999
students versus other size schools. Part B explains why many small schools have very
high costs. Among other duties, they provide specialized facilities and specialized staff
for their specialized student bodies. Thus very small schools often have very high costs
because of the extra services they provide. High costs per se do not mean inefficiency, if
the schools produce socially desirable outcomes. On the other hand, very large schools
Russell Harrison - Report on School Size and Education Outcomes - Page 41
often have high inefficiency ratios, since they produce social and academic problems that
minimize how well they teach their students versus what they cost.
What about the remaining in-between schools? In New Jersey the average school that
houses 500-999 students may enjoy significantly lower costs than do other size schools.
Part C focuses on four different indicators that can be used to compare housing costs
and education costs. It shows that for all these indices, schools of 1,500 or more students
may generate inflated costs. The super-sized schools are connected with higher costs for
housing students, as well as higher costs for educating students, especially after taking
into account how many students attend each school, rather than simply comparing
schools one by one.
Russell Harrison - Report on School Size and Education Outcomes - Page 42
SECTION 3A:
THE CUSTODIAL/ SCHOOL HOUSE FUNCTION VERSUS
THE EDUCATIONAL/ VALUE ADDED FUNCTION
COMPARING TWO TYPES OF COST/BENEFIT RATIOS
AS A FUNCTION OF SCHOOL SIZE:
To improve the validity and reliability of policy analysis, it is useful to build on
databases where the public has the opportunity to inspect the facts they report. In effect,
the underlying databases are subject to public review. In the present research project for
the Commission, ?transparency? and ?open access? were key criteria used to guide all
analyses. All underlying data must be publicly accessible for critical review.
This limited the research. Namely, neither the U.S. nor N.J. Departments of
Education report fiscal information for all individual schools. The NJ DOE only reports
expenditure and revenue information for districts, not schools. Thus it is not possible to
use publicly accessible information that directly estimate fiscal costs for each school in
New Jersey. Consequently, there is only limited data available to measure the effects of
school size solely on fiscal costs per school, since the data are rather crude.
Thus Section 4 pays attention to the possibility that bigger schools produce social and
academic costs in addition to fiscal costs. In fact, adding up six different types of costs
for different size schools, an important discovery was made. Big schools are associated
with much higher costs in aggregate, counting lower proficiencies in math, reading, and
writing as academic costs, dropouts and absenteeism as social costs, plus district-wide
spending as a fiscal cost.
To be more specific, these aggregate social, academic, and fiscal costs emerge over
time, comparing past enrollments to future agglomerations of costs. This clearly
indicates that school size is correlated with compounded inefficiency, and indeed
significantly so.
Section 4 also adds a quick look at a new indicator of ?residual inefficiency?. This
indicator measures how well high school students perform on reading tests, relative to
district spending and the socio-economic status of students. Namely, it sees how far
above or below they perform compared to expectations, looking at a subject area dear to
the governor?s heart.
These ?residual? performance levels are instructive, since they show what happens as
a function of school size over time. Namely, one sees that the ?residual? percent of
students who pass HSPT tests on reading is lower in larger schools. To repeat, these
results emerge comparing past enrollments to academic benefits several years in the
future, relative to fiscal costs. Over time, students in large schools do worse at learning
how to read, compared to what is spent on them in school, and depending on the
resources available to them in their home or community.
Some advocates of big schools, however, do not care about long-term effects from
school size. They are only interested in the ratio of costs per students in any given year.
They want to know what it costs to ?board? or ?house? a given number of students in any
given year. They want to know if ?big box? architecture is a cheaper way to provide
space for a given number of students in a given year. Their criterion is the ratio of total
spending, or total comparative costs, to total pupils on class rosters. They are little
concerned with whether students attend classes regularly, or even drop out over time, or
Russell Harrison - Report on School Size and Education Outcomes - Page 43
can pass even the most basic of proficiency tests. They are preoccupied with the
custodial role of schools. They want to know the ?bottom line?.
Using a simple criterion that compares total costs during each school year to total
pupil enrollment each Fall, they conclude that big districts are cheaper. Consequently,
they assume that big schools are cheaper, since big districts typically have big schools.
Taking the next leap of faith, they conclude that big districts and big schools are more
efficient, since their buildings house more students at lower cost.
Such conclusions ignore several emerging principles in modern educational outcome
evaluation research. Namely, there is a difference between short-term and long-term
costs. What may seem in the short run may prove quite expensive in the long run.
Secondly, looking at how much it costs to house a student for a given year ignores the
issue of how much it costs to help that student learn during the time they are housed in a
given school. There is a difference between cost-benefit ratios when one looks at the
quantity of schooling a student receives in a given year, versus the quality of learning
they obtain over several years.
Third, one must take into account the possibility that education research should look
at lagged relationships just like public health research. The architecture and organization
of schools ? like smoking ? does not produce symptoms that necessarily show up in one
day, one week, or one year. They only show up over time. Thus like smoking research,
one must look at long-term costs, and not just perceived short-term benefits. What is true
for public health research is also true for educational outcome research. Puffing away for
one year may not hurt much. Puffing away for many decades becomes literally a matter
of life and death. So does compulsory attendance in over-sized schools.
This supplemental report will apply these basic principles to educational cost/benefit
analysis. It will report what happens from extrapolating fiscal information for districts to
schools, and then looking at different fiscal cost/ academic benefit ratios.
The resulting evidence documents certain major conclusions about cost/benefit ratios
for New Jersey schools. Namely, the following conclusions seem valid:
?Big schools may reduce the short-term costs of housing students.
?Big schools emphatically increase the long-term costs of educating students.
?Big schools may reduce the short-term costs required to provide a certain gross
quantity of schooling, as measured by the number of students enrolled at the
beginning of a year.
?Big schools much more dramatically increase the long-term costs required to
provide a certain quality of learning. Namely big schools increase the long-term
costs required to help students meet acceptable (passing) levels of performance on
basic academic proficiencies, comparing school size in the past with performance
levels five or more years in the future. This is especially true if one takes into
account the large number of marginal students who drop out of big schools over
time, and thus obscure the true costs of obtaining a certain quality of academic
achievement per student originally enrolled.
These findings make use of recent conceptual breakthroughs in outcomes-based
education research. Erik Hanushek, Ludger Woessman, and other institutionalists have
applied these innovations in cross-national research plus cross-state research. These
Russell Harrison - Report on School Size and Education Outcomes - Page 44
methodological refinements have not yet been applied widely in studying intra-state
educational outcomes.
(1) It is absolutely essential to distinguish between the short term and long term
determinants of educational outcomes. Quite a few educational outcomes are
endogenous in the short run. It is only by looking at long term ?lagged?
relationships that one can untangle ?causal? relationships. [Metaphorically
speaking, what is cheap in the short run may be worthless in the long run, if the
product or service fails to produce any value. What is true for plumbing or
electrical firms is also true for schools. A big company may not always be better,
even if they offer a lower price for a unit of service. What is important is quality,
and what happens over time.]
(2) There is a big difference between what is required to maximize the short-term
quantity of schooling in any one year versus the long-term quality of what
students learn over time.
a. It seems easy to maximize short-term quantity: For example, the more
money that is spent in any one year, the more the number of students
enrolled in that year. This is almost tautological, in that most aid formulas
distribute educational funds based on reported enrollments. Thus it is not
so much that money increases enrollments, but enrollments increase
money, at least at the local level. In the short run, spending and the
quantity of schooling are closely linked.
b. The equation is more subtle for long term quality: Unlike the quantity of
schooling, the long-term relationships of spending with the quality of
schooling are much weaker. Increasingly it is not how much money is
spent, but how well, that determines the quality of spending. Thus nations
that spend the most per student often have extremely low relative levels of
achievement for the average student. This is especially true when one
compares the ratio of what the average student learns in the future
compared to what was spent per student in the past. It is also true when
one takes into account differences in class size versus school size. The
United States, for example, ranks extremely low in class size, compared to
other comparable nations. However, it ranks extremely high in school
size, except for a few nations like Korea that are attuned to Confucian
values. The United States spends a lot of money per student.
Unfortunately, compared to what is spent, the American student at any
given level of schooling displays inferior ?proficiencies?, compared to
many other comparable nations. Small classes cannot generally
compensate for large schools.
(3) Among the nations, the quality of schooling is the increasingly important
determinant of economic growth, development, and overall prosperity, not the
quantity of schooling. Thus increasingly how much money is spent on education
is not as important as how well it is spent, to increase the quality of learning per
unit of spending.
(4) Among the states, it is important to compare the tradeoffs of school size and class
size. Generally, states with larger schools have larger classes. However,
nationwide, if you cut school size by the same percent that you increase class
size, a state with the basic parameters of New Jersey would save over
$500,000,000 a year. However, not only fiscal costs but social costs would be
Russell Harrison - Report on School Size and Education Outcomes - Page 45
reduced. Such a policy would reduce the number of assaults on students and
teachers by over 10,000 over a decade, plus reduce hundreds of dropouts, plus
increase average test scores for thousands of students.
(5) Proof of these arguments is reserved to a follow-up study. In this report, I simply
want to clarify certain simple facts for New Jersey. Namely, the relationship of
school size with outcomes varies depending on whether the outcome measures
the short-term costs of housing students, versus the long-term costs of educating
students.
To clarify these distinctions, perhaps the following tables will help.
Table 3A1 contrasts the costs of educating a student versus the costs of housing a
student, and how to measure each function.Table 3A1: The Costs of Housing Students
versus the Costs of Educating Students
Where big schools appear
superior
Where small schools appear
superior
Unit Cost basis Custodial Costs of housing
students
Training Costs of
educating students
Short-term versus long-term
time perspective
Short-term impacts Long-term impacts
Value: quantity of
schooling, versus quality of
education
Quantity of schooling, as
measured by aggregate
student enrollment at the
beginning of a year
Quality of education, as
measured by the per cent of
high school students who
can pass proficiency tests
Cost/ benefit ratio Index of short-term housing
cost/benefit ratio:
The ratio of expenditures
over the course of a year
versus the number of
students enrolled at the
beginning of the same year.
In short, spending per
student in a given year.
Index of long-term
education cost/benefit
ratio:
The ratio of expenditures in
the past versus the percent
of high school students who
pass proficiency tests in the
future, looking at the future
The next two tables explore the degree to which school size is correlated with the
custodial costs of housing students ? at least in New Jersey.
To start, Table 3A2 looks only at short-term costs for a narrow range of functions.
That is, it matches up observed expenditures in 1996-1997 with enrollment totals in that
same year. It also looks only at certain ?comparative? costs per pupil, which ignores the
total educational costs faced by many schools. Table 3A2 shows that the cost of housing
students appears as a negative function of school size, if you look only at a limited range
of fiscal categories, and you ignore delayed effects that extend over time.
Russell Harrison - Report on School Size and Education Outcomes - Page 46
TABLE 3A2:
The ratio of fiscal costs in a given year
Divided by total enrollment at the beginning of the year
HOUSING COSTS AS A FUNCTION OF SCHOOL SIZE FOR HIGH SCHOOLS AND ALL SCHOOLS
One Year Housing costs = comparative cost expenditures divided by the pupils on class rosters, measuring
both with district totals for 1996-1997, then weighting results by individual schools in district
The ratio of expenditures to student enrollment is an index of "housing costs" during any one school year.
Here 1996 - 1997 data are used to measure both spending and enrollments.
Comparative Cost per Pupil [CCTOT_Y2] is taken from NJ DOE State Report Card.
The enrollment size in 1996-1997 is taken from U.S. DOE CCD file
Enrollment in
1996-1997
Secondary
school only in
SSD
Secondary
school only in
USD
All secondary
schools in any
type of district
except Charter,
Vocational,
Alternative/
Special districts
all schools of all types per cent
difference
of index
from
mean for
all
schools in
sample
0-499 Mean $9,943.60 $8,154.89 $8,356.89 $8,214.26 3.05
N 5 28 46 1,382
500-999 Mean $10,696.03 $7,877.16 $8,472.70 $7,583.68 -4.87
N 30 112 142 726
1000-1499 Mean $9,458.41 $7,710.46 $8,137.73 $7,762.63 -2.62
N 22 68 90 155
1500 + Mean $8,158.00 $7,454.94 $7,630.71 $7,549.22 -5.30
N 12 36 48 51
All Mean $9,805.51 $7,800.28 $8,239.91 $7,971.51
N 69 244 326 2,314
Range in Housing Cost index from
smallest to largest schools -8.34
Table 3A3 offers a more sophisticated view of custodial costs. First, it takes into
account the total costs that may be required for different types of students. Second, it
takes into account the possibility that cost functions may change over time. Doing so, it
shows that one type of school seems to display a particularly favorable pattern of
custodial costs over time. Namely, schools that house 500-999 students seems to have a
particularly favorable ratio of costs to enrollment over time, especially compared to
larger schools. The cost advantage of the schools with 500-999 students in 1996-1997 is
lower than larger schools not only in the short run, but in the long run. Indeed the cost
advantage of schools with 500-999 students versus larger schools seems to grow over
time.
Russell Harrison - Report on School Size and Education Outcomes - Page 47
Overall, mean average differences in ?total costs per students? differ significantly
among different size schools in New Jersey.
TABLE 3A3
mean average differences in ?total costs per students?
School
year = SY 1997 SY 1998 SY 1999 SY 2000
School size enrollment
categories in 1996-1997
0-499 Mean $9,477 $9,880 $10,172 $10,259
Median $8,937 $9,287 $9,517 $9,677
N 1382 1393 1406 1416
500-999 Mean $8,800 $9,319 $9,578 $9,770
Median $8,720 $9,053 $9,307 $9,462
N 726 726 726 726
1000-1499 Mean $9,096 $9,605 $9,945 $10,108
Median $8,842 $9,569 $9,915 $10,258
N 155 155 155 155
1500 & above Mean $8,895 $9,507 $9,787 $10,039
Median $8,937 $9,430 $9,672 $9,884
N 51 51 51 51
All schools with
data Mean $9,226 $9,679 $9,964 $10,093
Median $8,876 $9,238 $9,509 $9,657
N 2314 2325 2338 2348
500-999 schools versus: SY 1997 SY 1998 SY 1999 SY 2000
1000-1499
students mean $94.85 $187.51 $209.42 $269.69
1500 +
students mean $296.03 $285.70 $366.81 $337.80
500-999 schools versus:
1000-1499
students median $217.00 $377.00 $365.00 $422.00
1500 +
students median $122.00 $516.00 $608.00 $796.00
ANOVA F 12.15 7.52 7.63 5.67
Sig 0.001 0.000 0.000 0.000
Reject Null hypothesis at
.10, .05, and .001? yes yes yes yes
REPORT CARD FIELD TOTCOSTY_2 TOTCOSTY_3 TOTCOSTY_4 TOTCOSTY_5
Russell Harrison - Report on School Size and Education Outcomes - Page 48
Table 3A3 shows that over time a school size of 500-999 students is associated with
significant total cost savings per students versus schools housing 1,000-1499 students.
The mean savings in total costs of housing students range from $94.95 in year one to
$269.69 by year four. The median savings in total costs of housing students range fom
$217.00 in year one to $422.00 in year four.
The same table also shows savings versus schools of 1,500 or more students. The
mean savings in the total costs of housing students range from $296.03 in year one to
$337.80 by year four. The median savings in the total costs of housing students range
from $122.00 in year one to $796.00 by year four. Comparing four different categories
of school size, the differences of schools housing 500-999 students versus other size
categories are statistically significant at the .001 level of probability for each of the four
years analyzed.
Many other tables show even more significant cost savings when attention is paid not
just to the costs of housing students, but to the costs of educating students, and also take
into account the total number of students enrolled in each school in each size category.
Table 3A4 for example shows that the ratio of what it costs to what children learn grows
significantly in larger schools, comparing four size categories.
Section 3B explores in greater detail the relative merits of schools in the size range of
500-999 students, while Section 3C explores in greater detail the relative costs of schools
housing 1500 or more students.
Section 4 shows that the results are most emphatic when analysis takes into account
the full range of academic and social costs produced by larger schools. These include
social costs like dropouts and absenteeism, plus academic costs like failures on HSPT
tests of math, reading, and writing. Looking at different indices of ?compounded?
inefficiency and ?residual? inefficiency that adjust for the poverty, racial composition,
class size, and other traits of each school, school size is strongly correlated with a wide
constellation of inefficiency costs that must be borne by New Jersey tax payers.
Overall the evidence makes clear that the custodial costs of ?housing? students are
not as systematically related to school size as are the training costs of ?educating?
students. Educational Policy Makers and the public should insist that future research take
into account various ways that large schools reduce their ?custodial? costs of ?housing?
students by encouraging absenteeism on any given day, plus dropouts over time, to
exclude the marginal student who is hardest to house or educate.
Future research should explore the more subtle ways that large schools cut costs. For
example, in the short run many crowd more students into a given 1,000 square feet of
floor area. This cuts nominal costs. However, by the end of a four year cycle they may
have far fewer students per floor area, due to excessive attrition. This increases the costs
that must be borne by other agencies who deal with truants and dropouts, including
police, juvenile courts, welfare, and alternative schools.
Thus it is important to measure the effects of school size over time, and not just shortterm
cost/ benefit ratios. Over time the ratio of costs to benefits grows, as a function of
school size, especially if one compares comparable schools that exclude small ?other
schools? facing inflated costs due to ?special need? mandates.
Russell Harrison - Report on School Size and Education Outcomes - Page 49
Tables 3A4 and 3A5 move from the costs of measuring the costs of housing students
to the costs of educating students. It shows that in New Jersey, school size is linked to
training costs for educating high school students in particular. By looking only at
comparable schools that provide HSPT tests, and excluding ?other? schools, one sees
more clearly the links from school size to the costs of educating students.
Schools of 1,000 are more have significantly higher cost ratios for educating students.
In fact, the differences in cost/benefit ratios for educating students differ significantly
among the four key categories of school size utilized in this report. This is true even for a
cost index based on comparative costs versus total costs per students.
TABLE 3A4:
SCHOOL SIZE IN THE PAST IS LINKED TO HIGHER COSTS OF LEARNING AMONG NEW
JERSEY HIGH SCHOOLS IN THE FUTURE
A proof using unweighted data for individual schools serving mostly high school students
Comparing costs required for a one percent average increase in passing rates for math (HSPT)
proficiency tests - among schools with a majority of grade 9-12 students
RATIO OF PER PUPIL SPENDING VERSUS PER CENT PASSING MATH HSPT TEST,
MEASURING BOTH INDICES DURING 1999-2000,
but computing their average values for school size several years prior during 1996-1997
School Size Mean N
Per cent difference of index from mean
for all schools in sample
0-499 95.28 27 -3.42
500-999 96.35 138 -2.33
1000-1499 99.83 87 1.20
1500 and above 105.00 48 6.44
Total schools 98.65 300
Per cent Increase in the cost of learning index,
comparing the range from smallest to largest high
schools =
9.86
Russell Harrison - Report on School Size and Education Outcomes - Page 50
TABLE 3A5
Analysis of Variance for differences in Cost of Education Indexes
Comparing small and large High Schools
Using Data Weighted by Enrollments in each school
The Cost of Education Index =
Ratio of spending CCPP to % passing HSPT exam [READ], using data from 1999-2000
School Size for 1999-
2000
Mean Cost of
Education Index for
1999-2000
N
(weighted by
students in
each school
in 1999-
2000)
Std. Deviation
0 to 999 students in
2000 99.06 128,336 23.65
1000 or more students
in 2000 102.69 218,418 35.19
Total 101.35 346,754 31.46
ANOVA Table
Cost of Education Index as a function of school size in 1999-2000
Sum of Squares df Mean Square F Sig.
Between Groups
(combined) 1064139 1 1064139 1078.34 0.0000
Within Groups 342184981 346752 987
Total 343249120 346753
School Size for 1996-
1997
Mean Cost of
Education Index for
1999-2000
N of cases
(weighted by
students in
each school
in during
1996-1997)
Standard
Deviation
0-499 95.57 10,956 16.76
500-999 97.41 104,342 25.10
1000-1499 99.12 106,063 30.83
1500 + 106.38 92,846 40.23
Total 100.57 314,207 32.14
Cost of Education Index as a function of school size in 1996-1997
Sum of Squares df Mean Square F Sig.
Between Groups
(combined) 4680089 3 1560030 1532.39 0.0000
Within Groups 319870189 314203 1018
Total 324550277 314206
Russell Harrison - Report on School Size and Education Outcomes - Page 51
Summary of Section 3A
Such tables document several emerging themes for New Jersey
Larger schools may have, or appear to have, lower costs for housing students,
especially ignoring lost-term cots. However, larger schools have significantly higher
costs for educating students. These cost are especially clear if one looks at longer-term
relationships between school size and cost/benefit ratios.
In terms of short-term costs of housing students, the largest schools may appear to
have cost advantages over the smallest schools.
However, the relationship varies depending on the level of student and the type of
district. For all schools, the difference in the short-term costs of housing students may be
less than ten percent, as of 1996-1997. However, the relationship of school size with
costs is obscured.
Looking at long-term costs, various tables show a favorable picture for smaller
schools, even though many smaller schools are ?other? schools.
For custodial housing costs, the schools that house 500-999 students seem to have a
very favorable competitive advantage versus larger schools, especially over time.
For the costs of educating students, the pattern is even more more consistent. now
The costs of educating students are lower in all schools of less than 1,000. In contrast, the
costs of educating students are higher in schools housing above 1,000 students. This can
be seen clearly looking at high school data.
Among schools serving a majority of high school students, the long-term costs of
educating students is about ten percent less in the smallest schools versus the largest
schools, looking at schools where most students are in regular grades 9-12. Using unweighted
data, the biggest schools cost more than the smallest schools.
Table 3A5 shows the results of taking enrollments into account. It uses cost data
that is weighted by the enrollment in each school. Now school size is significantly
correlated with the education cost index, an index that measures the relative costs of
educating students to pass basic HSPT exams. Larger schools have higher costs for
educating students to achieve the same results as smaller schools. It costs more to raise
the passing rate by one per cent.
The relationship of school size in 1996-1997 to the index of educational costs for
1999-2000 is statistically significant. That is, there are statistically significant differences
among the mean average for this cost index comparing all four key categories of school
size. However, this index is looking at value added, quality, or education outcomes, for
math in particular.
In the next section I look more closely at differences in other cost indexes for schools
housing 500-999 students in particular.
Russell Harrison - Report on School Size and Education Outcomes - Page 52
SECTION 3B
Linkages From School Size To The Costs Of ?Housing? Students - Schools
Housing 500-999 Students Have Significantly Lower Total Costs Per Pupil
Advocates of big schools sometimes complain that very small schools, with fewer
than 500 students, often report very high costs per student, at least on average. This leads
to a frequent conclusion that small schools in general cost a lot, and perhaps are
inefficient. However, such a conclusion is too simplistic for many reasons.
As this Section emphasizes, other small schools ? namely those that house between
500 and 999 students - may spend very little.
More importantly, it is important to recognize the special burdens and unique
academic challenges faced by many small schools housing fewer than 500 students.
These unique burdens inflate the costs faced by the very small schools, when one
computes average spending per school.
First, the very small schools provide training for a much larger relative share of
?ungraded? students. Such students are often certified special needs students. Such
students receive and require extra monies mandated by federal and state law. They
require a high ratio of staff to students. Parents and staff often ask for special equipment
and more easily accessible buildings and classrooms. Such obligations inflate costs,
which are hard to amortize for small schools serving specialized student bodies and
facing rapidly evolving legal mandates.
Perhaps such problems should be documented. Namely, small schools housing fewer
than 500 students have a significantly higher mean average percent of ungraded students,
at least in New Jersey. Relative to other schools, they housed 11.55% more ungraded
students during 1996-1997. The absolute difference was statistically significant at the
.037 level of probability, with an F value of 4.372, for 2,119 schools surveyed during
1996-1997. It is true that many larger schools house a large absolute number of ungraded
students. However, very small schools on average house a larger relative concentration
of such students. This share of special students increases the costs per student.
The fact that small schools that house fewer than 500 students face extra burdens can
be documented in another way. They are disproportionately required to operate as ?other
schools,? whether their students are classified as ungraded or not. Small schools with
fewer than 500 pupils are much less likely to serve as traditional elementary and
secondary schools, compared to schools of 500 or more pupils. In New Jersey small
schools disproportionately serve students in special education, alternate schools, charter
schools, and vocational schools, which comprise and define the ?other? schools.
Among regular schools, 42.34 percent house 500 or more students. Among ?other?
schools, only 3.66 percent house 500 or more students. Small schools, with less than 500
students, are many more times likely to operate as ?other schools? serving very
specialized student bodies. The differences in roles are statistically significant.
Why is this important? The "other" schools must deal with vastly inflated costs,
which usually demand far higher spending levels. The data is clear, looking at 1996-97
and 1999-2000 as base years.
On average, regular schools spent respectively $8,885.06 and $9,793.84 during 1996-
97 and 1999-2000. On average, the ?other? schools spent respectively $15,876.00 and
Russell Harrison - Report on School Size and Education Outcomes - Page 53
$14,570.51 during the 1997 and 2000 school years. Thus the ?other? schools spent
respectively 78.68 per cent more during 1996-1997, and 48.77 percent more than the
regular schools during 1999-2000. (This latter change partially reflected the growth of
charter schools, which spend less on average than even regular schools).
On average, ?special education? schools spent 175 to 185 per cent more than the state
average per student, during the base years. On average, ?vocational? schools spent from
57% to 33% more than the state average during those years. On average, ?alternate?
schools spent from 5 to 7% more. Among the ?other? schools, only charter schools spent
less than the state average, since they were only funded at 90%, and were often brand
new facilities.
However, even though they do not necessarily spend a lot, charter schools often face
special problems, like other small schools. In many cities, charter schools
overwhelmingly serve minority student bodies. Statewide, charter school districts enroll
a significantly larger share of minority (African-American and Hispanic) students than do
other districts. The charter schools face major start-up problems not faced by older
schools. Charter schools have to hire, pay rent for facilities, scramble to buy new
equipment, and face extra paper work challenges. Thus the charter school life cycle
explains extra problems faced by some small schools. These normally would produce
extra costs, except for funding lids placed on charter schools.
Overall, ?other? schools in New Jersey tend to be very small, and small specialized
schools face major fiscal burdens. They serve students formally classed as special
education students placed in ungraded classrooms. They serve special education students
who are mainstreamed. They serve other students who are placed in ?alternate? settings,
or receive special ?vocational? training, or are otherwise different.
Overall, small schools face much different academic and social burdens than many
larger schools. These burdens help explain why they appear to spend so much, at least in
the short run.
However, the fact that some small schools spend a lot on average does not necessarily
mean that such schools cost the state or even local taxpayers a lot of money, relative to
the total educational budget for the state and district. The reason is that many of the
schools with the most unique burdens are often extremely small. If one weights for the
number of students involved in each school, then smaller schools in general will be seen
not to cost very much, per student, relative to the state average for all schools.
Their impact is quite different from the very large schools. Namely, schools with
1,500 or more students spend more than smaller schools, if one takes into account the
number of students enrolled in each school. Small schools that spend a lot have few
students. Big schools that spend a lot have large enrollments. Weighting school
expenditures by enrollment, schools with 1,500 students or more in 1996-1997 spent
$265.49 more per student on average than other schools collectively during 1999-2000.
Thus large schools during 1996-1997 were spending significantly more by 1999-2000, at
the .05 significance level.
The inflated expenditures of the biggest schools are even more noticeable if one takes
into account their dropout patterns. If one adjusts expenditures by dropout patterns, then
schools with 1,500 or more students spend dramatically more than other schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 54
However, when one compares enrollments for individual schools, and simply
compares schools without taking into account their differential dropouts, an interesting
pattern emerges for schools with 500-999 students. This size category displays a
favorable pattern for total costs per pupil, based on state financial records. Namely, the
average schools in this enrollment category spend less than all other schools collectively,
which include both the very small schools (with less than 500 students) and larger
schools (with more than 1000 students). Schools with 500-999 students spend less than
smaller and larger schools, and thus less than the state average.
One reason is simply that small schools with 500-1000 students face fewer of the
unique challenges of the other even smaller schools serving fewer than 500 students. To
house their students and meet their challenges, schools with 500-999 students do not have
to spend a lot more than other schools. In fact, they spend a lot less than other schools.
The following table compares average spending for schools housing from 500 to 999
students, versus all other schools, based on fiscal data for two different base years.
Total costs per
student during
1996-1997
Total costs per
student during
1999-2000
School with 500-999
students during 1996-1997
Mean
$8799.82 $9769.74
N 726 726
School with larger (or
smaller) student bodies
during 1996-1997
Mean
$9421.50 $10237.54
N 1588 1622
How much less was spent
in schools with 500-999
students than in other
schools?
-$621.68 -$467.79
Totals for schools of all
sizes
Mean
$9226.45 $10092.89
N 2314 2348
Russell Harrison - Report on School Size and Education Outcomes - Page 55
The table shows that during 1996-1997, schools with 500-999 students spend $621.68
less per student.
During 1999-2000, several years later, the schools with 500-999 students during
1996-1997 still spent $467.79 less per student.
[Of course, it should be noted that the two sets of school are not identical for 1996-
1997 versus 1999-200. The latter base year includes fiscal data for a new set of charter
schools. Over time other changes occurred as well (since over time some schools close
while others open)].
For both years the differences in spending were statistically significant at the .05 level
of probability. The following ANOVA (analysis of variance) tables compare variation in
mean spending (on total costs per pupil) to document that schools housing 500-999
students differ significantly from other size schools.
ANOVA Table for 1996-1997 spending relative to school size in 1996-1997
Sum of
Squares
Df
Mean
Square
F Sig.
1996-1997
total costs per
student
Between
Groups
(combined)
192557665.2 1 1.93E+08 30.805 0.00
Within Groups 14452174838 2312 6250941
Total 14644732504 2313
ANOVA Table for 1999-2000 spending relative to school size in 1996-1997
Sum of
Squares
Df
Mean
Square
F Sig.
1999-2000
total costs
per pupil
Between
Groups
(combined)
109747629 1 1.1E+08 16.229 0.00
Within Groups 15864700528 2346 6762447
Total 15974448157 2347
The following tables use multivariate regression analysis to confirm the pattern of
relatively low costs for New Jersey schools with 500 ? 999 students. The first table
models 1996-1997 total costs per student as a function not only of school size, but also
the percent poor and percent minority students in each school. The same pattern emerges
as from a bivariate regression analysis. Schools with 500-999 students during 1996-1997
spent significantly less than other schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 56
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
B Std. Error Beta
(Constant) 8601.916 44.647 192.666 0.00
Schools with 500-
999 students for 96-
97 (big500) -225.644 59.054 -0.081 -3.821 0.00
% free lunch
eligible for 97-97
(pctpoor) -6.263 2.16 -0.126 -2.899 0.00
percent minority ?
(poverty and
minority from US
DOE CCD for
1997-97) pctmin) 14.961 1.788 0.364 8.366 0.00
The next multivariate regression table confirms this pattern of relatively low costs for
New Jersey schools with 500 ? 999 students. It models 1999-2000 total costs per student
as a function both of school size, plus the percent poor and percent minority students in
each school. The same pattern emerges as from a bivariate analysis. Schools with 500-
999 students during 1996-1997 spent significantly than other schools, this time looking
several years in the future.
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
B Std. Error Beta
(Constant) 9154.038 42.891 213.425 0.00
Schools with 500-
999 students for
1996-97 (big500) -191.16 56.732 -0.065 -3.37 0.00
% free lunch
eligible for 1996-
1997 (pctpoor) 5.649 2.075 0.107 2.722 0.01
percent minority -
from US DOE CCD
for 1996-97 -
(pctmin) 16.841 1.718 0.388 9.802 0.00
Russell Harrison - Report on School Size and Education Outcomes - Page 57
Summary of 3B
How do NJ schools with 500 ? 999 students compare to other schools? The
following table summarizes four slope coefficients that estimate multiplier effects. The
slopes summarize how much would have been saved per student in the other schools if
they had spent like schools in the 500-999 enrollment category. The bivariate
coefficients ignore the fact that school size may affect future patterns of race and poverty,
and ignore all other control variables as well. The partial slopes reflect the results of
controlling for poverty and race in each school during 1996-1997. Both bivariate and
multivariate coefficients estimate responses in total costs per pupil to school size during
1996-1997, for lagged and unlagged spending.
The cost savings from the enrollment size target ranges from about $200 to $600 per
student. For a given state with 1,000,000 public school students, such numbers could add
up to major savings for taxpayers.
Of course, better schools might also encourage certain parents to reduce their out of
pocket spending in favor of public schools. Many students in private schools might
transfer to public schools, if the problems that beset many larger public schools could be
bypassed or minimized. Thus a shift to smaller public schools, versus the compulsion to
expand schools housing 1000, 1500, or even more students, might have a range of effects.
Russell Harrison - Report on School Size and Education Outcomes - Page 58
Hypothetical savings if "other" schools had spent like schools
with 500-999 students
(multiplier effects measured by four slope coefficients)
$0.00
$100.00
$200.00
$300.00
$400.00
$500.00
$600.00
$700.00
Student costs as a
function of 96-97 school
size
Hypothetical savings if
"other" schools had
spent like schools with
500-999 students
(multiplier effects
measured by 4 slope
coefficients)
$621.68 $491.36 $225.64 $191.16
1996-1997
tcpp ($),
bivariate
1999-2000
tcpp ($),
bivariate
1996-1997
tcpp ($),
multivariate
1999-2000
tcpp ($),
multivariate
Russell Harrison - Report on School Size and Education Outcomes - Page 59
Conclusions from 3B
This analysis reviews how much schools spend to fund total costs per pupil, and
whether there is any specific school size category that seems to minimize costs.
All the indicators reported here achieve statistically significant linkages with a
specific school size category. The results enable one to reject a hypothesis of random
results at the .05 level of probability. Namely, schools that enroll between 500 and 999
students spend significantly less than all other schools for the two different base years.
Such schools seem to lie in a lucky latitude between the Scylla and Charybdis faced
by other schools. Schools that are even smaller often serve specialized student bodies
with special needs. Federal and state regulations inflate costs. Such costs are not easily
amortized over their specialized student bodies. On the other hand, many educators
justify such costs, since special students often require more personal settings for
successful outcomes relative to their individualized goals.
At the other extreme are certain very large schools. They face inflated costs because
of disproportionate problems of crime, violence, dropouts, and absenteeism. Schools that
lack a strong climate of connectedness and trust generate such problems. Such problems
especially burden very large schools, including schools in the 1000 above category, and
perhaps especially schools in the 1500 and above size categories.
However, between Scylla and Charybdis are schools that house 500 to 999 students.
The evidence indicates that they meet their obligations at a very reasonable cost, at least
compared to other New Jersey schools. Such evidence should be taken into account
when deciding enrollment targets for schools to follow that seek to minimize fiscal costs,
social costs, and academic costs.
Further research should explore in greater detail whether separate analyses of
elementary and secondary schools will document similar patterns of evidence. Future
research should be funded to confirm that high schools that house between 500 and 999
students have an extremely favorable cost structure, especially when one takes into
account their ability to retain entering students through to graduation.
This report does not measure value added, or which size school produces the best
academic and social benefits compared to how much it spends.
This analysis thus ignores how well the school performs. It just looks at how much
the district spends relative to each school and each student to fund its housing function.
The task here is to report how much it costs to house the average pupil. The specific
task is to identify a specific size category of schools that seems to produce an extremely
favorable cost function. This report focuses on indicators that measure total spending per
pupil, or what it costs to house a student who is still enrolled in the school. Future
research is needed to take into account what it costs per student, when one takes into
account how many students drop out over time for each school.
I also leave to other reports the task of evaluating how much it costs to educate the
average pupil, and how best to model education costs as a function of school size. To
understand cost functions, it is important not only to look at what it costs to house
students, including those who are prone to absenteeism and dropouts. It is also important
to look at how much they learn while in school, as shown by test results. However, a
discussion of various ways to measure those cost indicators is left to other reports.
Russell Harrison - Report on School Size and Education Outcomes - Page 60
Here the focus is on very simple cost indicators. They rely on district spending that is
allocated to each school in the state, to estimate per student expenditures, and more
specifically total costs per pupil, as a function of school size. No attempt was made, for
example, to exclude transportation costs, much less specific functions provided by
?other? schools.
Prior to further research, one can make an important policy conclusion. School size is
linked to many different cost indicators, and the public deserves to be informed of these
patterns.
Russell Harrison - Report on School Size and Education Outcomes - Page 61
SECTION 3C
A CLOSER LOOK AT FOUR SCHOOL COST INDICES
FOR VERY BIG SCHOOLS OF 1,500 OR MORE STUDENTS
Linking School Size to Four Indices that Measure
The Costs of Housing Students,
And more importantly the costs of Educating Students
To measure the true costs of educating students, the public must distinguish the costs
of housing students versus the costs of educating students. They must distinguish the
short-term (nominal) costs of housing students versus the long-term and indirect costs of
educating students. To measure costs, the public should take into account the costs
exported to other agencies by schools that encourage dropouts.
The public should realize that some schools export long-term costs by pushing out
marginal students, students who fail to thrive, students who fail to learn. By getting rid
of these marginal students, an individual school can lower its nominal rate of spending, -
even though societal costs are escalated.
The public should recognize the extra costs produced by schools that generate
disproportionate dropouts, both official and unofficial. Such schools produce extra costs
for outside agencies like local police stations, probations, courts, welfare offices,
AFDC/TANF, child protective services, juvenile lockup facilities, alternative schools,
?juvenile resource centers?, mental health agencies. Such costs should be taken into
account.
In terms of cost accounting, it is nearly irrelevant how schools push out students.
Some emphasize active short-term efforts, some emphasize long-term neglect. In either
case, student dropouts become the responsibility of other agencies that must house or
help the rejects, or ignore their failure. The costs of neglect should be recognized by
adjusting short-term rates of nominal spending to take into account long-term rates.
External costs should be added to internal costs. Costs should reflect dropouts.
The costs of how well a school houses students should take into account what
happens to those students and student problems they export to other agencies. Schools
should be charged for their failures to retain students, and especially their de facto
dropouts, even if they fail to report them as de jure dropouts. The costs to society should
take into account what happens to each student cohort between grades 9 and 12, and all
those who fail to reach grade 12.
This report shows that school size is closely linked to real costs, especially when the
public looks at the extra costs produced by the largest schools of 1,500 or more students.
Such costs become particularly clear given two accounting improvements:
?The public or an appropriate state agency adjusts the total costs of housing
students to include the costs faced by outside agencies like local juvenile facilities
and alternative schools who must house dropouts from dysfunctional schools.
?The public or an appropriate state agency further adjusts costs by taking into
account the goal of educating students, which means helping them learn how to
pass basic high school proficiency tests - as opposed to simply housing them for a
few years.
Overall, this report shows the results of using four different types of indices to
measure costs.
Russell Harrison - Report on School Size and Education Outcomes - Page 62
Indexes 1 and 2 provide two different ways to measure the costs of housing students,
or how much it costs per student to keep their name listed on the class roster. The first
index is the traditional na?e index. The latter is much better.
1. Index 1 simply measures unadjusted expenditures per student, and ignores
how many students drop out over time.
2. Index 2 adjusts expenditures per student to take into account dropouts, both de
jure and de facto. This index takes into account extra costs imposed on other
agencies to deal with official and unofficial dropouts. Such dropouts
disproportionately move into the care of juvenile courts, Jamesburg, the
welfare system, public health facilities, and other institutions that must deal
with educational rejects from dysfunctional schools. Index 2 takes into
account the pattern of dropouts, by using a standard index of dropout rates that
compares grade 9 to grade 12 students. Those who disappear between grades
9 and 12 are counted as de facto dropouts. In turn, index 2 multiplies Index 1
by the reciprocal of the dropout index. This helps project what the district and
other agencies would be paying, if they all paid the same amount to house
each student per year. Index 2 charges schools for their failures, though not
the significantly higher costs that dropouts at Jamesburg and county lockups
and welfare agencies actually require. At present, Index 2 is reported only for
high schools. In the future, similar indices should be constructed for other
levels of schooling, in addition to high schools.
Indexes 3 and 4 parallel indexes 1 and 2. They provide two alternative ways to
estimate the costs of educating students, or how much it costs per student to increase the
passing rate by one percent. Drawing on Indexes 1 and 2 respectively, indexes 3 and 4
provide estimates using unadjusted and adjusted expenditure data.
3. Index 3 measures the ratio of Unadjusted Expenditures per student to the
percent of students who pass basic proficiency tests. In effect, it measures the
costs per student of increasing the passing rate by one per cent.
4. Index 4 measures the ratio of Adjusted expenditures per student to proficiency
passing rates, after taking into account the costs for other agencies for dealing
with the dropouts and transfers caused by school pathologies. It provides the
best estimate for measuring the true total costs per student, though it is the
hardest to obtain complete information to compute the index.
To understand the full costs of housing students, the public should take into account
the number of students who leave after each year of school, and never reach their senior
year.
In doing so, it is important to look at patterns of change over time. A big school in
one year may not be a big school 2, 4, or 10 years later, and vice versa. To measure
school size, one should look at school size in the past, and then evaluate its effects over
time. It is misleading to measure school size in the present, before size has a chance to
impact the evolution of a school climate.
Big schools lose students year after year, so they have far fewer students who reach
their senior year than began their careers in grade 9. Big schools retain far fewer students
to the end of a four-year high school education than they enrolled at the beginning. The
adjusted costs of housing students should take into account these failures.
Russell Harrison - Report on School Size and Education Outcomes - Page 63
To measure the costs of educating students, the public should also find out if the
remaining students actually learn anything while in school. Big school students often
become experts in how to survive highly escalated rates of school crime and violence.
However, the issue is how much they learn about reading, writing, and arithmetic.
Previous costs studies have been simplistic and na?e. Previous studies have only
looked at unadjusted costs. They ignore how many students have been kicked out,
pushed away, or simply run away from the school into the care of other agencies. Worse,
previous studies generally ignore whether the students who remain housed within a
school over the four-year high school cycle actually learn anything or not.
This is the first study to systematically compare these four indices of school costs.
This study will test a prediction that a clearer pattern emerges when one looks at the
more sophisticated indexes to account for costs. The public will see more clearly that the
very largest schools do not cost less, but more. Big schools can cut nominal costs by
crowding a lot of ninth grade students into a limited amount of floor area. However, by
the twelfth grade large numbers will drop out. Of those who remain, large numbers fail
to pass basic proficiency tests. They have failed to thrive, and have failed to learn.
In assessing true school costs, the public and the state should move beyond nominal
costs, and look at the real costs of education. If so, the adverse effects of big box schools
become clear. Big box schools may not cost a lot to house students short term, because
they house more students per 1,000 square feet, at least during the first months that
students are exposed to the school. In the long run the big school also appear to cost less,
because they export the costs of the students they fail, who become the ward of other
agencies. Big schools no longer have to pay to house these students, and especially
marginal students. Thus their nominal costs in the future are low, versus smaller schools
that better retain all students.
The nominal costs of big schools are low for another reason. They do not teach their
students very much, nor even control their behavior. Big schools do not pay the costs of
police, probations, judges, and others who must intervene to deal with school problems,
but are financed from non-school budgets.
The public should measure costs not only from students who are lost from class
rosters. Costs extend to those students who are not lost from the school but simply fail to
thrive there. Schools also lose students who lose their innate potential to succeed, when
schools fail to teach the students who remain. Society and the student both lose when
students fail to master basic academic proficiencies, so they can not pass even simple
tests.
By looking at true costs, the inefficiency of big schools becomes clear. They fail to
retain students in their classrooms over time. Even among those they retain, they fail to
educate those students to read, write, or do simple arithmetic. When one looks at sins of
omission as well as sins of commission, the true costs of big schools emerge.
Russell Harrison - Report on School Size and Education Outcomes - Page 64
Five different tables in this section (Tables 31C 1- 5) illustrate the linkages of school
size with the four different types of indices. In these tables each index has a specific
meaning.
Index 1 measures the unadjusted costs of housing students in the short-run, ignoring
dropouts.
This index is computed for all schools. However, it should at least be weighted
by the number of students in each school, for a very important reason. Very small
schools frequently seem to cost the state a great deal, even though the serve very
few students. Often these schools that seem to cost the most are very small
?special needs? schools serving ?high risk? students. Even if cost indexes are not
adjusted for dropouts over time, cost indexes should take into account the number
of students served by each school. Thus Index 1 and all the other indexes are
weighted by student enrollments.
Index 2 measures adjusted costs, based on retentions.
Index 2 is adjusted for how many students each school retains over time, and
especially between grades 9 and 12. It takes into account the costs that should be
borne by schools that lose lots of students between grades 9 and 12. Since index
2 is based on retention and loss patterns among grades 9 and 12, it only includes
schools serving such students. Thus the number of students covered is less than
for Index 1.
Index 3 and 4 adjust for actual learning.
Index 3 and 4 move on to take into account how much students learn.
Since Indexes 3 and 4 use HSPT tests to measure learning, they are by necessity
limited almost exclusively to high school students. Thus they are based on data
for fewer students and schools than is Index 1. In particular, Index 4 is limited,
because it only includes schools with grade 9 and 12 students, and schools that
report HSPT tests, which some special schools do not.
However, even regular schools may also serve other grades. Some schools with
HSPT tests and students in grades 9 and 12 also have other students. They may
not be comparable to schools limited almost exclusively to students in grades 9
through 12. Thus Indices 3 and 4 can be applied more precisely.
Tables 3C3 - 5 are refined even beyond Tables 3C1-2.
Tables 3C3-5 move on to look at more comparable schools, namely high schools
with 90% of more high school students. These tables exclude schools serving
large numbers of ungraded special needs students. These tables also exclude
schools with lots of pre-high school students, who are often funded at different
levels.
In summary, Tables 3C3-5 look at high schools weighted in terms of how many
students they actually serve, that have 90% of more high school students in that
initial cohort, and that report test scores to allow one to evaluate how well
students learn over time.
A Preview
All the Tables show the same pattern. The more refined the estimates of costs, the
more significant is the impact of school size. Very large schools produce very large
costs. However, in terms of educating students, school size has a basic monotonic
relationship with how much it costs to teach students to master basic high school
proficiencies. School size is significantly correlated over time with how much students
learn in their academic careers, or rather, how little.
Russell Harrison - Report on School Size and Education Outcomes - Page 65
Taking into account how many students stay in school over time, and how much they
learn, big schools cost more over time. Certain small schools serving certain types of
high-risk students may cost a lot. However, looking at all the students in each school, big
schools generally cost more, and usually significantly more.
Table 3C1 shows that schools of 1,500 and above cost more both to house and
educate students, taking into account the number of students enrolled in each school. The
costs are very similar if you ignore dropouts, but if you pay attention to dropouts, the cost
differences are staggering. The big schools cost 17 percent more to house students, and
36 per cent more to educate students, on average ? after adjusting for dropouts and how
much students actually learn who remain in school.
Russell Harrison - Report on School Size and Education Outcomes - Page 66
TABLE 3C1
Mean Averages for four cost indexes during 1999-2000, classified as a function of prior
school size during 1996-1997
The Degree to which Large High Schools face increased costs both for housing and educating students
Measuring the link from school size to future costs during the time period it normally take for a first year
student cohort to graduate from high school [the period from grade 9 to grade 12]
0-1499
students in
1996-1997
1500 and above
student in 1996-
1997
All schools in
sample during
1996-1997
% Cost
increase in
largest
schools over
1,500
Index 1 Index 1
Costs of Housing
student
(Unadjusted for
dropouts)
Dollars spent (on average) to "house" pupil
Total Comparative Cost
per Pupil CCTOT_Y5
99-00 or ccps9900
"Comparative"
spending per pupil $8,437.43 $8,449.76 $8,438.46 0.15
Index 2 Index 2
Costs of Housing
student
(Adjusted for
dropouts)
Dollars spent (on average) to "house" pupil
ADJ_CC00
"Comparative
spending" per
pupil $11,045.63 $12,935.55 $11,604.78 17.11
Index 3 Index 3
Costs of Educating
student
(Unadjusted for
dropouts)
Dollars per pupil (on average) required to increase HSPT by 1
%
rr_math = ccps9900/
hspt030 (math) Math $98.14 $106.38 $100.57 8.41
rr_read = ccps9900/
hspt029 (read) Reading $101.00 $112.49 $104.40 11.38
rr_write = ccps9900/
hspt031 (writing) Writing $98.38 $104.38 $100.15 6.10
Average for math,
reading, writing All three $99.17 $107.75 $101.71 8.63
Index 4 Index 4
Costs of Educating
student
(Adjusted for
dropouts)
Dollars per pupil (on average) required to increase HSPT by 1
%
RR_MATH2 (uses
adj_cc00) Math 124.99 169.58 138.20 35.68
RR_READ2 Reading 129.17 181.37 144.63 40.41
RR_WRIT2 Writing 124.85 165.26 136.82 32.37
Average for math,
reading, writing All three 126.34 172.07 139.88 36.15
Russell Harrison - Report on School Size and Education Outcomes - Page 67
Table 3C2 shows that the differences in costs for Big versus Small schools are not
random. In fact, the differences are highly significant statistically. Moreover, in terms of
the number of students involved, the differences are certainly worthy of consideration
and appropriate reaction in the highest circles of government.
TABLE 3C2
The Statistical Significance of Greater Costs in large versus small schools, using 1,500 as a
tipping point
Mean Averages for four cost indexes during 1999-2000, classified as a function of weighted
school size during 1996-1997
The Degree to which Large Schools of 1,500 or more students lead to increased costs - both for
housing and educating students - especially for high schools
Index 1 F ratio Sig. Level Df = N - 1
Each indexes measures a different
N of students during 1996-1997
(for schools with data for 1996-
1997 through 1999-2000)
(unadjusted
for dropouts)
Costs of
Housing
student
"comparative"
spending per
pupil 8.89 0.00288 1,166,231
Index 1 is not limited to high
schools. It includes all schools
with "comparative costs per pupil"
in 1999-2000 and enrollment data
in 1996-1997. This excludes new
schools after 1997, and schools that
closed. Here it is computed for
1,166,232 students.
Index 2 F Sig. df
(adjusted for
dropouts)
Costs of
Housing
student
"comparative
spending" per
pupil 13183.45 0.00000 308,011
Index 2 adjusts for potential
students lost between grades 9 and
12 (ie, de facto dropouts). This
reduces sample size since normally
only high schools offer grades 9
though 12. Here Index 2 is
computed for 308,012 students.
Index 3 F Sig. df
(unadjusted
for dropouts)
Math 4368.63 0.00000 314,206
Reading 6492.04 0.00000 314,206
Costs of
Educating
student
Writing 2438.37 0.00000 314,206
Index 3 does not adjust for de facto
dropouts. However, it does adjust
for HSPT passing rates. This
reduces the potential sample size
since mostly high schools report
HSPT tests. Note that Index 3 may
include more students than either
index 2 or 4, which require
adjustment data for grade 9 and 12
students.
Index 4 F Sig. df
(adjusted for
dropouts)
Math 17363.35 0.00000 307,696
Reading 19497.57 0.00000 307,696
Costs of
Educating
student
Writing 16155.60 0.00000 307,696
Index 4 adjusts for both HSPT test
scores and de facto dropouts. This
twice reduces the sample size since
normally only regular high schools
report data on all these topics.
Russell Harrison - Report on School Size and Education Outcomes - Page 68
The next tables further explore differences in costs, using a more refined sample of
high schools.
Table 3C3 evaluates costs using index 3, but only for high schools with 90% or more
regular high school students enrolled in grades 9-12.
As before:
?Index 3 compares what it costs per student to increase by one percent the students
able to pass various HSPT proficiency tests.
?Index 3 does not adjust expenditures for students who have dropped out or been
pushed out of the school.
?The expenditures and test scores are based on data reported for the 1999-2000
school year. They measure the costs of educating each student during 1999-2000.
?This index is compared to the original size of each school during 1996-1997,
while each school is weighted by student enrollment during 1996-1997 to
estimate per student patterns.
?Overall, the results show lagged effects from school size over time, at least for a
specific index of costs relative to HSPT proficiencies.
Table 3C3: The Mean average costs of educating high school students by school size,
for four categories of school size
The marginal
unadjusted costs of
educating students
to learn
Math Proficiencies
The marginal
unadjusted costs
of educating
students to learn
Reading
Proficiencies
The marginal
unadjusted costs of
educating students
to learn Writing
Proficiencies
School size in
1996-1997
N (weight) =
enrollment in
each school in
1996-1997
rr_math =
ccps9900/ hspt030.
rr_read =
ccps9900/
hspt029.
rr_write =
ccps9900/ hspt031
0-499 10,956 95.5685 96.3959 96.2349
500-999 104,342 97.4087 100.4964 98.2459
1000-4999 106,063 99.1170 101.9698 98.7276
1500 & above 92,846 106.3848 112.4922 104.3811
Total 314,207 100.5736 104.3954 100.1513
Russell Harrison - Report on School Size and Education Outcomes - Page 69
Table 3C3 shows that the costs of educating students is higher in the larger size
schools, using Index 3. This contrast emerges for every subject matter, for every possible
comparison of size categories. School size is not simply important comparing schools
larger or smaller than 1,500 students.
Table 3C4 evaluates the degree to which the results for Index 3 are statistically
significant. This table shows that for every subject area analyzed, the mean cost of
educating students is significantly higher. The costs are not just higher on average, but
significantly higher, in the larger schools.
TABLE 3C4: ANOVA Table for Index 3 as a function of school size in the past
SPSS variables
ANOVA
Comparisons
Sum of Squares Df =
N ? 1
Students
Mean
Square
F Sig.
The costs of educating high school students to master high school level math
proficiencies
Between
Groups
4680089. 3 1560030 1532 .000
Within Groups 319870188 314203 1018
rr_math =
ccps9900/ hspt030
Total 324550277 314206
The costs of educating high school students to master high school level reading
proficiencies
Between
Groups
8998120 3 2999373 2256 .000
Within Groups 417788146 314203 1330
rr_read =
ccps9900/ hspt029
Total 426786265 314206
The costs of educating high school students to master high school level writing
proficiencies
Between
Groups
2422971 3 807657 836 .000
Within Groups 303765997 314203 967
rr_write =
ccps9900/ hspt031
Total 306188968 314206
The next figure ?graphs? the results for the math index. The Figure shows that over
time bigger schools generate a higher mean average cost of educating students to learn
math. Though Figure E summarizes the pattern for math, similar results apply to reading
and writing. The costs to educate students escalate for larger schools. Big schools are
no bargain.
Figure 3C5, like prior tables, compares what happens during the period from 1996-
1997 through 1999-2000. This covers a period it takes a successful grade 9 class to reach
grade 12 status. Future research should take a look at other cohorts to demonstrate
similar results.
Future research should report in much greater detail the inefficiencies produced by
big schools. They should explore even more sophisticated indexes of ?compounded
inefficiency? that take into account social problems facing students and teachers like
dropouts and absenteeism, as well as failing test scores compounded with high
expenditures.
This is the task of the next section.
Russell Harrison - Report on School Size and Education Outcomes - Page 70
Figure 3C5:
A Picture of Index 3 Education Costs by School Size
Schools that were larger during 1996-1997
Face higher costs for educating students
During 1999-2000
x
90.00
92.00
94.00
96.00
98.00
100.00
102.00
104.00
106.00
108.00
Index 3 for math, by school size
[2000 cost ratios versus 1997
weighted school size
Ratio of comparative costs per pupil versus the %
passing Math HSPT test during 1999-2000,
classified by student enrollment during 1996-1997
Ratio of
comparative costs
per pupil versus %
passing HSPT test,
weighted by
student enrollment
95.57 97.41 99.12 106.38
0-499
500-
999
1000-
1499
1500 +
Russell Harrison - Report on School Size and Education Outcomes - Page 71
SECTION 4: - ?Compounded? Inefficiency and ?Residual?
Inefficiency
The tables in section 4 provide statistical evidence for New Jersey that school size is
significantly linked to the costs of educating students. It looks first at indices of
?compounded inefficiency?, and then at indices of ?residual inefficiency.?
The results show that the relationships of school size with inefficiency outcomes are
strong and consistent. The evidence easily rejects the null hypothesis ? that the
relationship of school size with the cost of educating students is random.
School size is significantly correlated with an index of ?compounded inefficiency?
that includes six different components academic, social, and fiscal costs. It measures not
only three sets of academic failures, but also dropouts and absenteeism as social failures
by schools, as well as the costs of housing students in each school.
The first three sets of tables look respectively at differences in average levels of
?compounded Inefficiency? These tables document a wide range of significant
relationships.
The fourth set of tables show the results of using an alternative index of ?residual
inefficiency?. It shows that as school size increases, net (residual) value added decreases.
Reading is a key subject dear to the governor?s heart. Where schools are bigger, schools
show a decreasing ability to add value added to the task of helping children learn to read,
relative to what one would expect knowing their race, poverty, level of spending within
the school, class size.
Many prior studies suggest that school size will be linked to inefficiency costs and
declining value added. The hypothetical evidence is borne out in reality. Rather than
discuss the results in detail, here is a quick outline:
4.1: Looking at Bivariate Relationships, the Differences in Inefficiency between
Schools of Different Size are Sufficient to Reject Null Hypotheses regarding Size-
Inefficiency Relationships
For example, the differences in inefficiency between regular high schools of different
sizes are statistically significant at the .05 level of probability.
Table 4.1: Larger schools have much higher inefficiency problems overall than
do smaller schools, comparing mean Compounded Inefficiency scores for High
Schools
?Schools with 1,000 or more students have dramatically worse problems of
inefficiency, as shown by student inability to master basic academic
proficiencies, plus symptoms of anomie and alienation like dropouts and
absenteeism, even though the total costs per student may be high
?Regular high schools suffer from a much more dramatic increment in
inefficiency scores as a function of school size than do Vocational-Technical
schools.
4.2: A simple graph provides a clear picture of major differences in overall inefficiency
between different size categories of schools, using 1000 students as a tipping point
Figure 4.2: In NJ Overall Inefficiency is far greater in larger schools with 1,000
or more students, as measured by the combination of high total costs per pupil,
high dropout rates, high absenteeism, and low student proficiencies in reading,
math, and writing
Russell Harrison - Report on School Size and Education Outcomes - Page 72
4.3: Multiple Regression Coefficients that document significant linkages over time
between school size and overall inefficiency, after controlling for class size, federal aid,
ungraded students, poverty, mobility, minority, student computer ratios, and faculty
training
Table 4.3 Regression analysis shows that school size has statistically
significant relationship with higher levels of educational inefficiency
among New Jersey high schools, ?all things else equal?, so that the null
hypothesis can be rejected at the .05 and .01 levels of probability
Table 4.1a: Larger schools have much higher inefficiency problems overall than do smaller
schools, comparing mean Compounded Inefficiency scores for High Schools
TYPE OF SCHOOL
SCHOOL
SIZE
Mean for
Index of
"compounded
inefficiency"
index
Inefficiency
Index for
different size
schools as a %
of average for
this type of
school of any
size
Relative per
cent greater
inefficiency in
large high
schools (above
1000) versus
small high
schools
Number of
schools with data
for HSPT test
scores, plus
dropouts,
attendance, and
total costs per
students
Both regular
and vocational
high schools
0 ? 999
students -0.092 -13.806 189
Both regular
and vocational
high schools
1,000 or
more
students 1.685 252.548 141
Both regular
and vocational
high schools
Any Size
enrollment 0.667 x 266.35 330
High school
(regular)
0 - 999
students -0.311 -53.221 168
High school
(regular)
1,000 or
more
students 1.665 285.188 139
High school
(regular)
Any Size
enrollment 0.584 338.41 307
Vocational-
Technical with
HS students
0 - 999
students 1.657 93.203 21
Vocational-
Technical with
HS students
1,000 or
more
students 3.046 171.370 2
Vocational-
Technical with
HS students
Any Size
enrollment 1.778 x 78.17 23
Russell Harrison - Report on School Size and Education Outcomes - Page 73
Table 4.1b
Methodology for Table 4.1a
Going beyond Section 1, Section 4 expands the universe/ sample of cases to include
vocational-technical schools that were not listed as high schools in both the 1996-1997
and 1999-2000 CCD surveys.
The universe of cases for Section 4 includes all schools with relevant high school "cost"
data for 1999-2000 and enrollment data for 1996-1997:
It includes schools serving high school level students even though not classified as a
?mainstream? or ?regular? high school for both 1996-97 and 1999-2000. Thus it includes
certain vocational-technical schools serving high school students, and providing HSPT
tests for those students.
Table 4.1 and Figure 4.2 includes 330 high schools that include 307 regular schools and
23 vocational technical schools. Of these 189 enrolled less than 1,000 students in 1996-
1997, and 141 enrolled 1,000 or more students.
The task was to measure linkages from school size in the past (1996-1997) with
compounded inefficiency in the future (1999-2000).
The compounded inefficiency index takes into account total costs per student as well as
dropouts, poor attendance, and poor test scores on reading, math, and writing.
The compounded inefficiency index is based on the sum of six z scores.
(1-3) % of students who fail to pass HSPT examinations on math, reading, writing,
(4) poor retention rates (high dropout rates),
(5) poor attendance rates,
(6) paralleled by high total costs per student.
For Table 4.3 some of these schools lack predictors used in multiple regression analysis.
Thus the sample size in Table 4.3 is smaller than the sample for Table 4.1.
For the schools analyzed:
?Schools with 1,000 or more students have dramatically worse records of inefficiency, as
shown by student inability to master basic academic proficiencies, plus symptoms of anomie
and alienation like dropouts and absenteeism, even though the total costs per student may
be high.
?Regular high schools suffer from a much more dramatic increment in inefficiency scores as a
function of school size than do Vocational-Technical schools. However, Voc-Tech schools
are much fewer in number than regular schools, and they may not report dropouts,
absenteeism, and proficiency test failures in the same manner as comprehensive high
schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 74
Figure 4.2a: In NJ Overall Inefficiency is far greater in large schools
with 1,000 or more students
Larger schools have greater inefficiency in NJ -
Comparing all schools serving HSPT level students
-50.000
0.000
50.000
100.000
150.000
200.000
250.000
300.000
Inefficiency Index for different
size schools as a % of
average for this type of school
-13.806 252.548
Russell Harrison - Report on School Size and Education Outcomes - Page 75
Figure 4.2 continued::
In figure 4.2 the schools include both ?regular? high schools and vocational-technical high
schools. The total of 330 schools includes 307 ?regular? high schools and 23 ?vocationaltechnical?
schools.
The Inefficiency Index = sum of z scores for 6 "cost" indicators with the following coefficients:
+ total costs per pupil
+ dropout rates
- attendance rates
- HSPT reading test
- HSPT math test
- HSPT writing test
Note that each z score is computed separately for all schools in state with data. Thus N varies for
the individual components.
However, the composite index is limited to schools serving high school level students taking
HSPT tests.
Russell Harrison - Report on School Size and Education Outcomes - Page 76
TABLE 4.3 - Regression analysis shows that School size has a statistically significant relationship
with higher levels of educational inefficiency among New Jersey High Schools, "all things else equal"
Results of Multiple
regression Analysis
Unstandardized
Coefficients
Unstandardized
Coefficients
Standardized
Coefficients
Standardized
Coefficients Sig. Coefficient
B = slope
Std. Error of
estimate
[about slope]
Beta t-ratio
Measure of
"statistical
significance"
Is coefficient
significant at
.05 level of
probability?
At the .01
level?
Constant:
[Hypothetical value of
DV if all IV were set to
zero]
-5.2451 1.1231 -4.6702 0.000
Independent Variables
(predictors)
1996-97 % faculty with
BA/BS degrees only -0.0055 0.0127 -0.0173 -0.4356 0.663 no, no
1997-98 Student
Computer Ratios -0.0124 0.0144 -0.0302 -0.8571 0.392 no, no
% minority in school for
1996-97 0.0282 0.0103 0.1894 2.7399 0.007 yes, yes
Mobility rate for 1996-97 0.1505 0.0235 0.3086 6.3926 0.000 yes, yes
% free lunch eligible
(with NA=0) for 1996-97 0.0429 0.0216 0.1613 1.9905 0.047 yes, no
% ungraded students
[with missing = 0] for
1996-97
0.0309 0.0423 0.0287 0.7309 0.465 no, no
% federal revenues for
1999-00 0.7273 0.1908 0.2355 3.8117 0.000 yes, yes
Class size - average for
1996-97 0.0185 0.0497 0.0133 0.3729 0.710 no, no
School size = total
student enrollment
for 1996-1997
school year
0.0010 0.0003 0.1121 2.9295 0.004 yes, yes
The Independent Variables (predictors) are listed in the order they appear on the SPSS Regression
"Enter" command. To ensure conservative values, School Size was listed last on the enter
command.
Nevertheless School Size is positively and significantly correlated with higher Compounded
Inefficiency Scores, comparing all New Jersey High Schools in this sample.
Russell Harrison - Report on School Size and Education Outcomes - Page 77
SECTION 4.4 -
The need for even more compelling evidence
Future research should develop a new type of statistical evidence to prove that school
size is significantly linked to efficiency outcomes, especially for at risk students.
It is predicted that a new type of coefficient will clarify even better how and where
and when to reject a null hypothesis about the relationship of school size and efficiency
outcomes.
The new research should measure partial relationships between school size and the
efficiency of the educational production function, and obtain ?residuals? for reading test
scores and other outcomes. These ?residuals? would identify schools that perform better
or worse than expectations, based on their total comparative costs per pupil, class size,
teachers with BA or BS degrees, mobility rates, as well as the socio-economic status of
students.
First I outline how to measure this new index of efficiency, and the need to focus on
poverty and minority districts.
Figure 4.4 summarizes the expected results of measuring this new type of efficiency
coefficient as a function of school size and poverty students.
Future research should be commissioned to implement this methodology for all levels
of schooling, and for all types of outcomes, including efficiency scores on math and
writing as well as reading skills, plus efficiency in dealing with problems of absenteeism
and dropouts.
Russell Harrison - Report on School Size and Education Outcomes - Page 78
A New Way to Measure Efficiency Coefficients
Inefficiency can be measured by residual test scores that are lower than the level to be
expected from the amount of money spent on students, class size, teacher training, and
social and economic determinants of achievement. Inefficiency means low mean
averages for residuals. Efficiency means high mean averages for residuals. Efficiency
means schools do better than expected from the resources available to them, including
how much money is spent on each student..
New research should be undertaken to document that among poverty schools in New
Jersey, school size is especially conducive to inefficiency. Larger schools have more
inefficiency. Smaller schools have more efficiency. That is, they have residual test
scores far higher than can be explained by resources like money, class size, and the socioeconomic
status of their students.
Among "poverty" schools, school size is significantly correlated with "residual" test
scores that vary from the level to be predicted from the resources present in each school.
In poverty schools, size hurts efficiency.
The ?residuals? should be computed using lagged variables. For example, predictors
could use data for school years three years in the past. Consequently, the results would
show the effects of school size on efficiency outcomes three years in the future.
Research should then focus on districts and schools with significant poverty
concentrations and/or major poverty concentrations, to show what happens to efficiency
outcomes where schools are over-sized, using this new index of efficiency.
Figure 4.4 shows the results. It produces major implications:
?The Commission of Business Efficiency in the Public Schools should fund
follow-up research to confirm that school size can indeed explain differences in
efficiency outcomes that range up to 800% improvements for students in smaller
schools, versus an 800% deterioration in efficiency outcomes for larger schools,
relative to where the school should be.
?The Commission on Business Efficiency in the Public Schools should fund a
follow-up study to document that school size significantly and specifically thwarts
the promise of a ?thorough and efficient? education for poverty and minority
students, contrary to explicit guarantees in the New Jersey constitution.
?The Legislature, the Executive, and the Courts must confront a growing problem
that does not revolve around money per se, but defective organizational structures
for the administration and governance of primary and secondary education, and
perhaps beyond.
Russell Harrison - Report on School Size and Education Outcomes - Page 79
Table 4.4:
Hypothesized results of measuring
Mean efficiency scores for each school size category
as a % of the overall mean score for all comparable schools,
looking at "residual" HSPT scores.
-1,000.0000
-800.0000
-600.0000
-400.0000
-200.0000
0.0000
200.0000
400.0000
600.0000
800.0000
1,000.0000
School size categories based on enrollment three years in the past
Efficiency scores by school size
Efficiency in teaching reading skills as
a function of school size:
Mean efficiency scores for each school
size category are measured as a % of
the overall mean score for all
comparable schools, looking at
"residual" HSPT scores.
806.5401 250.1841 8.5733 -832.0889
0- 499 students 500-999 students 1000-1499 students
1500 and up
students
Russell Harrison - Report on School Size and Education Outcomes - Page 80
SECTION 5 - Where to Find the Evidence
This Section has three parts.
?Section 5A explains the importance of high schools which define the universe of
interest for this initial report.
?Section 5Bsummarizes major data sources.
?Section 5C outlines criteria for selection of 100% Comprehensive Samples.
?Section 5D summarizes the number of cases used to link school size with test
scores, violence, and compounded inefficiency.
Russell Harrison - Report on School Size and Education Outcomes - Page 81
SECTION 5A
SELECTING THE SAMPLE,
WHAT THE SAMPLE SHOWS,
AND WHAT FUTURE SAMPLES SHOULD EXPLORE
What is the relationship of school size with achievement test scores, school violence,
and inefficiency in educating students? Is there evidence for New Jersey schools that
would enable one to reject a null hypothesis for each relationship?
For this initial needs assessment, a decision was made to focus on high schools. One
reason is that problems of anomie and alienation have serious consequences in high
schools. Student violence and school crime literally become matters of life and death.
Moreover, high school students are more apt to skip school or be absent on their own
volition. They are also likely to get into major problems with the law while playing
hooky, more so than grammar school students staying home from an inner ear infection.
Thus both misbehavior in school and absenteeism from school can have serious
immediate consequences for high school students.
The combination of poor grades and dropout risks are also serious problems in high
schools. In high school, far more so than earlier grades, students performing poorly or
missing class are much more likely to leave school. Poor grades, absenteeism, and
dropouts push students off the ladder to middle class prospects into a culture of poverty
from which escape is difficult. In the culture of poverty they face a morass of problems
for themselves and for society as a whole. Areas with more dropouts are especially prone
to suffer from problems like births to unmarried females, homicides that lead to
incarceration in adult prisons for males, deficient care for children, both unborn and born,
and elevated risks of infant death. Tax payers face extra costs for public health care and
corrections where dropout rates escalate.
Communities face special problems where problems of academic failure, low test
scores, student violence, school crime, absenteeism, dropouts, are combined with inflated
school budgets. Parents of high school students tend to have a longer earning record and
larger savings than parents of elementary children. They are more apt to own or consider
home ownership, and are especially sensitive to local tax burdens to fund schools. If
schools are both expensive and ineffective, they are apt to vote ?with their feet?. Parents
of high school students are especially prone to flee an inefficient school system,
especially where options are close at hand.
This loss of middle class families from the school and the larger community further
compounds the problem of academic progress for those left behind, and impedes the
realization of vital educational goals.
Many variables shape educational problems. However, this research was designed to
test a theory that school size is a major exogenous variable shaping endogenous problems
that plague public school systems, including high schools.
If this theory is valid, then large schools and school size should be seen as major
explanations for problems of overall inefficiency at the high school level. To the extent
relationships of school size with such problems are highly significant, then public
officials in New Jersey should take heed in future debates about educational best
practices, optimal architectural design, and rational planning for education governance
and administration.
Russell Harrison - Report on School Size and Education Outcomes - Page 82
Based on the evidence for New Jersey high schools, school size is a major force
shaping educational outcomes that concern state legislators like Assemblyman Louis
Greenwald and members of the Commission on Business Efficiency of the public
Schools.
Section 1 of this project estimates relationships of school size with test scores on high
school proficiency tests. The tests measure student success in mastering math, science,
and writing skills respectively.
The first set of tables shows that large schools have significantly lower test scores.
Small schools have significantly higher test scores.
A graph visualizes some of the differences among schools of different size.
The last set of tables shows that the negative relationship of school size with test
scores persists for MRA coefficients. The coefficients are all statistically significant,
controlling for poverty, race, class size, expenditures, and various school resources.
The null hypothesis can be emphatically rejected for New Jersey high schools.
Section 2 of this project estimates relationships of school size with student violence.
The evidence is clear, looking at a sample of high school districts in New Jersey.
The size of district schools is positively correlated with the concentration of student
violence and school crime in a given district. This result is analogous to prior research on
school segregation. The author has previously shown that school size is significantly
correlated with the concentration of poverty children over time, comparing one school
versus another. This new research shows that school size is also significantly correlated
with the concentration of violence and crime in one district versus others. The size of the
average school in each district is significantly correlated with violence and overall
criminal incidents for districts serving a majority high-school students.
The first set of tables measures mean differences in violence, that is, bivariate
relationships. The ANOVA coefficients document statistically significant relationships.
A subsequent figure visualizes differences in violence as a function of school size.
The last set of tables show that results remain significant analyzing regression
coefficients that measure ?ceteris paribus? relationships.
The null hypothesis can be emphatically rejected for this sample of New Jersey high
school districts.
Sections 3 and 4 of this report correlate school size with different indices of school
costs.
Section 3 compares the costs of housing students versus the costs of educating
students. Schools that house 500-999 students seem to have a favorable spending pattern,
when one looks at total custodial costs per student, and especially over time.
Section 4 focuses on composite indicators that measure not only fiscal costs but also
social and academic costs. They include standardized scores for fiscal costs as measured
by total costs per student. They also include social costs as measured by high rates of
dropouts and absenteeism. In addition, they measure academic costs including poor
performance on math, science, and writing tests. The relationships with school size were
measured using lagged coefficients.
Russell Harrison - Report on School Size and Education Outcomes - Page 83
The first table shows that big schools have much higher inefficiency scores, both for
regular high schools and vocational high schools. Looking at regular high schools, the
differences in inefficiency score are significant.
A subsequent figure visualizes those differences.
The third set of tables shows that the same results hold for multivariate regression
analysis, which measures relationships ?ceteris paribus?. The null hypothesis can be
emphatically rejected for this sample.
The last table illustrates a prototype measure of ?residual? inefficiency. It measures
the gaps between where students should be performing on reading tests, and where they
actually perform. The expected level is a function of the poverty and race of students,
plus resources like spending.
In small schools, students perform above expectations. In large schools, students
perform worse than they should.
Overall, the present research protocol produces highly significant results. However,
follow-up efforts are desirable to answer remaining questions.
Do similar findings apply to all schools at all levels, statewide? Are the effects of
school size equally adverse in middle schools, in grammar schools, in alternative
schools?
What is the correlation of school size with the loss of middle class students or
families from districts? To what extent is school size correlated with changes in
demographics that independently harm educational progress?
Do similar findings apply to schools in urban, suburban, and rural areas respectively?
Are big schools especially harmful in center city districts?
Which tipping points significantly escalate problems facing public schools? To what
extent do schools of some 500-999 students surpass the achievement of schools in the
1000-1499 and 1500 and above enrollment categories?
To what extent does school size escalate the adverse effects of poverty on test scores,
in accord with the Howley-Bickel theory of educational inequality? Does New Jersey
follow the same pattern as other states in the South and West? Are the effects of school
size especially adverse in poor communities?
How far do the harmful effects of school size extend over time? Does school size
have maximum effects in the very short term, like one year, perhaps an interim term like
2-3 years, or even a longer term? Does school size set into motion certain internal
dynamics that corrupts the school culture for long periods of time, or at least the time
period required for a given student cohort to move through the various high school
grades?
What would be the aggregate costs savings of comparable trade offs in school size
versus options like class size? How many hundreds of million dollars would be saved
over time by statewide options such as a one to one tradeoff in school and class size, like
a reduction in school size of 1-10% versus an increase in school size of 1-10%? Would
the fiscal savings be matched by savings in social costs from less school crime, less
violence, less absenteeism, fewer dropouts? Would the fiscal savings be matched by
Russell Harrison - Report on School Size and Education Outcomes - Page 84
savings in academic costs like fewer student failures in mastering basic skills, and less
need for remedial classes?
To what extent would a reduction in student enrollment per floor area surpass a
reduction in student enrollment per teacher as a means to improve school operations with
minimal fiscal costs and maximum social and academic benefits?
To what extent are the alleged cost savings of big schools achieved by encouraging
dropouts and absenteeism by marginal students, and minimal learning by students who
stay in school?
What are key psychological traits that help explain the adverse effects of large
schools? To what extent is school size associated with the loss of connectedness, trust,
and social capital in the school community, with subsequent major implications for
adolescent health risks in a public health perspective?
Other countries like New Zealand and England have tried major reforms to overcome
the adverse effects of impersonal, oversized, factory-model schools. One option is the
proliferation of focus or academy schools to maximize school choice within a public
school setting. Which types of focus or academic schools or patterns of choice are most
correlated with significantly elevated levels of student proficiencies, controlling for
student poverty, race, class size, spending?
Russell Harrison - Report on School Size and Education Outcomes - Page 85
Section 5B: Sources of Data Used to Produce Tables
Data
Source
Publication/ Publisher Section 1 Section 2 Section 3 URL Address
1 U.S. Department of Education,
National Center for
Educational Statistics,
Common Core of Data survey,
1996-1997
(a) for all of
Section 1
(b) for all of Section
2. [c] used to
define
predominantly HS
districts
Table 3.3 (a)
enrollment (e,f)
race, ungraded
http://nces.ed.gov/ccd/
2 U.S. Department of Education,
National Center for
Educational Statistics,
Common Core of Data survey,
1999-2000
x x Section 3 http://nces.ed.gov/ccd/
3 New Jersey Department of
Education, Violence,
Vandalism and Substance
Abuse in New Jersey Schools
- 1999-2000
x All of Section 2. Composite
Inefficiency
Index
http://www.state.nj.us/njded/schools/v
andv/9900/append_d.htm;http://www.
state.nj.us/njded/schools/vandv/9900/
4 New Jersey Department of
Education, New Jersey Vital
Education Statistics
x Table 2.3 Table 3.3
(district data)
www.stte.nj.us/njded/data/vitaled/
S.Y. district information for 2000-2001
and 01-02.The district data for 2001-
2002 used in Table 2.3 were taken
from Vital Statistics sources.
5 Evalsoft, for the New Jersey
Department of Education,
School Report Card System
x x x http://nj.evalsoft.com/njDOE/data_ma
ps4632.asp;http://nj.evalsoft.com/njD
OE/files/Tables_to_Sections_to_Repo
rtCards.xls web sites provide direct
access to data, plus "road maps" to
explain both school and district data
5 School data: grade 11
statewide assessment results
from SC_tst11
All of Section
1
x Composite
Inefficiency
Index
read_yx = per cent students who pass
HSPT 99-00 (read_y6)
5 School data: grade 11
statewide assessment results
from SC_tst11
All of Section
1
x Composite
Inefficiency
Index
math_yx = per cent students who
pass HSPT 99-00 (math_y6)
5 School data: grade 11
statewide assessment results
from SC_tst11
All of Section
1
x Composite
Inefficiency
Index
write_yx = per cent students who pass
HSPT 99-00 (write_y6)
5 School data: grade 11
statewide assessment results
from SC_tst11
x x Composite
Inefficiency
Index
attendance rate att_yx where x = 1 to
7 (99-00)
5 School data: grade 11
statewide assessment results
from SC_tst11
x x Composite
Inefficiency
Index
dropout rate drop_yx where x = 1 to 7
(99-00)
5
5 School data: grade 11
statewide assessment results
from SC_tst11
Table 1.3 x x mobility rate mob_yx where x = 1 to 7
(96-97 for lagged)
5 School data: grade 11
statewide assessment results
from SC_tst11
x x Table 3.3 class size clsz_yx where x = 1 to 7
(96-97 for lagged)
5 School data: grade 11
statewide assessment results
from SC_tst11
Table 1.3 x x student-faculty ratio stfa_yx where x =
1 to 7 (96-97 for lagged)
5 School data: grade 11
statewide assessment results
from SC_tst11
Table 1.3 x Table 3.3 % faculty with BA/BS ba_yx where x =
1 to 7 (96-97 for lagged)
Russell Harrison - Report on School Size and Education Outcomes - Page 86
5 School data: grade 11
statewide assessment results
from SC_tst11
x x Table 3.3 student computer ratio stcomp_yx
where x = 1 to 7 (96-97 for lagged)
5 District fiscal data for 1999-
2000
Table 1.3 x x expenditures: total or comparative
costs per student in 2000 = tcps or
ccps
5 District fiscal data for 1999-
2000
Table 1.3 x x federal aid, state aid, local revenues
in 2000
1 The U.S. Department of Education provided the Common Core of Data CD for the 1996-1997 school year. I used this
source to measure (a) school enrollment to match up with "lagged indices" of test scores, violence, dropouts, absenteeism,
and costs for 1999-2000. (b) Mean average school size for each district during 1996-1997, total district enrollment divided
by the total number of schools, for 1996-1997 regular schools (c) the proportion of students in grades 9-12 to total
enrollment (totstu) - the index used to select out the 50+ districts with majority high school enrollment (d) alternate indexes
of student/ teacher ratios [tch_rto] and expenditures per student [expps] (e) racial composition (% by race, % minority) (f)
% ungraded students
2 The U.S. Department of Education provided Common Core of Data for districts during 1999-2000. District data used
include percent Asian students, percent white students, and percent students eligible for free lunch or reduced price lunch.
3 Violence includes simple assault, aggravated assault, fight, gang fight, robbery extortion, sex offense, threat. It excludes
weapons, vandalism, and substance abuse.
Russell Harrison - Report on School Size and Education Outcomes - Page 87
Section 5C:
Description of Samples used in Various Tables -Criteria for selection
.
?In this research the samples used for each table focus on high school students, to refute
claims that only elementary or middle school students are affected by size variables. It
should be noted that certain types of behavioral risk problems associated with school size
have particularly serious consequences for high school students. In New Jersey, school
size is significantly correlated with a wide range of serious consequences including poor
test scores, violence, and a pattern of inefficiency which produces problems like
dropouts, absenteeism poor test scores on math, reading, and writing ? in spite of high
levels of expenditures per student.
?Unless otherwise stipulated, every sample includes all schools or districts in the state
with available data for all the variables of interest in the table. Every table includes
school size as an independent variable, and one or more dependent variables. In each
section the first ?table? compares average scores for the dependent variable, after
classifying schools or districts by the size of the individual school, or the average school
in a district. The second ?figure? provides differences in mean averages using a graphic
format. In each section the third table reports regression analysis results. These results
?control for? and ?take into account? various background variables that also affect school
outcomes. These equations subtract out the effects of various variables that measure
race, ethnicity, income, poverty, fiscal resources, class size, computer accessibility,
teacher training, etc. The control variables are listed in the individual table, and also in a
summary of variables used for all tables.
?Each sample uses data easily available for inspection and review by the public. The URL
addresses are provided where all data can be obtained. Schools or districts lacking data
are excluded from the analysis. The goal was to focus on variables easily available in
?report cards? either from the federal or state governments. The intention is to encourage
members of the public to undertake their own analyses.
?Each sample is a comprehensive or exhaustive sample, subject to the stated criteria for
each table. The sample includes 100 per cent of the defined universe of cases. The
selection process is completely objective. The members of each sample are not
dependent on a "draw", or arbitrary ?matching? or subjective ?selection?. Thus they are
far superior to quota samples or convenience samples used in certain other research.
There is no selection bias possible, since every ?sample? includes cases that define the
?universe? of interest.
?Each table (or sample) is restricted to schools or districts with complete information for all
variables. For comparisons of mean averages, the sample generally includes all schools
or districts, since there is very little missing information, except for certain special needs,
vocational, or charter schools. For the regression analyses (Table 1.3, 2.3, 3.3) the
sample may be smaller, since missing data for one or more of the ?control variables? may
eliminate the school or district from the analysis.
?In short, the sample size depends only on the availability of publicly available,
"transparent" data, for the schools or districts indicated. It is therefore a 100% sample of
relevant cases with complete information on all data items of interest from reliable state
and federal sources.
?Sections 1 and 3 both analyze over 300 high schools. The section 1 high schools are
listed as high schools in both the 1996-1997 and 1999-2000 CCD surveys. The section 2
high schools include vocational-technical schools.
?The sample of school districts analyzed in Section 2 includes 51 districts with a majority
of high school students. It features regional high school districts with a majority of
students in grades 9-12 in 1996-1997. Grouped by county, they range from Greater Egg
Harbor Regional and Mainland Regional in Atlantic County to High Point Regional,
Kittatinny Regional, Lenape Valley Regional, and Wallkill Valley Regional in Sussex
County. The other schools are found in Bergen, Burlington, Camden, Cape May,
Cumberland, Essex, Gloucester, Hunterdon, Monmouth, Morris, Ocean, Passaic, and
Somerset Counties.
Russell Harrison - Report on School Size and Education Outcomes - Page 88
?Section 2 only analyzes High School districts. However, if one looks at all 2,348 schools
statewide with relevant data, a significant positive correlation will be found that links
school size with the % of violent incidents affecting each school, the implications of which
will be spelled out in future research.
Russell Harrison - Report on School Size and Education Outcomes - Page 89
Section 5D:
The Number of Cases in Each Table
Section 1 Tables for Schools?
Test scores
Table
1.1, also
figure 1.2
332 schools reported HSPT passing rates for math, reading, and writing in
1999-2000, and also had data available on enrollments for 1996-1997.
The number of schools in each category of school size (enrollment) in 1996-
1997 were:
Number of
schools
0-500 58
500-1000 139
1000-1500 87
1,500 and above 48
Total 309
The sample was further refined to focus on regular high schools.
Using ANOVA, the differences in test scores among different size categories
was highly significant for all three proficiencies tested. Thus the null
hypothesis is rejected for each subject area tested. School size in the past
is closely linked to poor test scores in the future.
Table 1.3
The regression equation includes 300 schools, since several schools lacked
complete data on one or more control variables. The 300 schools analyzed
have complete data for all variables, including the "control" variables.
These control variables take into account and subtract out confounding
influences due to spending, federal aid, class size, student/faculty ratios,
teacher education (% teachers with only undergraduate degrees), student
mobility rates, and % un-graded students.
All things else equal, the relationship of school size with each set of test
scores is statistically significant at the .05 level of probability.
Russell Harrison - Report on School Size and Education Outcomes - Page 90
Section 2 Tables for Districts?
Concentration of Violence
Table 2.1
The ANOVA sample includes 51 school districts with a majority of students
in grades 9-12. These are defined as the High school districts of interest for
this analysis. It measures the concentration of violence in each district,
relative to the average (mean) size of schools in that district three years
previously. The analysis of variance compares districts above and below
1000 students enrolled in the mean average school.
51 ?high school? districts classified by the average school size
in each district during 1996-1997
Number of
districts
0-999 students 34
1000 and above students 17
Total 51
Also
figure
2.2
Table 2.1b, and Figure 2.2, standardize the violence indices. Each district is
analyzed to report the degree that the differences or variances for that
district fall above or below the state average for all comparable districts,
expressed as a percent of the state average. Some districts are above, and
some are below, that baseline average.
The concentration of violence in each district, and the degree to which the
violence index is above or below the state average, varies significantly
between districts with different sized schools. The size of schools in the past
is closely linked to the concentration of violence within a district in the future.
The differences are statistically significant, and the null hypothesis must be
rejected.
Table 2.3
(a,b,c,d)
The regression equation includes 48 districts, since 3 districts were lacking
complete data. The remaining districts report complete data for all variables.
The control variables include overall district size (versus school size), per
cent Asian students, per cent Non-Hispanic "white" students, per cent
eligible for free lunch or reduced price lunch (an index of household poverty),
comparative cost per pupil, % students eligible for special education, local
taxes as a proportion of revenue sources (versus federal or state aid), the
student/ teacher ratio (certified staff only).
All things else equal, the relationship of school size with district violence is
statistically significant at the .05 level of probability. School size in the past
is closely linked to the concentration of violence within a district in the future.
It should be noted that if one looks at all 2,348 schools statewide
with relevant data for 1996-97 and 1999-2000, a significant
positive correlation will be found that links school size with the
% of violent incidents affecting each school in the future. The
implications of this pattern and the need for public access to
such data should be spelled out in future research.
Russell Harrison - Report on School Size and Education Outcomes - Page 91
Section 4 Tables for Schools?
Compounded Inefficiency
Table 4.1
In New Jersey over 300 schools enroll a majority of high school students.
They include not only "regular" high schools but also "vocational-technical"
high schools.
However, not all these schools report full data for dropouts, attendance, test
scores, and total costs per student that define the overall composite index of
"compounded inefficiency".
For these tables, 330 "regular" and vocational-technical high schools
reported full data for all variables, which could be used for ANOVA tables.
School Size category Number of
Schools
Both regular and vocational high schools
0-999 189
1000 and above 141
total 330
Regular high schools only
0-999 168
1000 and above 139
total 307
Vocational-technical schools
0-999 21
1000 and above 2
total 23
Figure
4.2
Figure 3.2 standardizes the compounded inefficiency indexes, to report
differences or variances for each school, to see how far the school is above
or below the state average for all comparable schools.
These differences or variances are measured as a % of the statewide
average. However, they can be above or below that average, since the
index measures relative differences or variances.
The differences in "compounded inefficiency" between different size schools
are statistically significant at the .05 probability level (based on ANOVA
results available from the author), and the null hypothesis must be rejected.
Both regular and vocational high schools classified by enrollments in 1996-
1997
School Size category Number of
Schools
0-999 students 189
1000 and above students 141
Total schools in sample 330
Russell Harrison - Report on School Size and Education Outcomes - Page 92
Table 4.3
The regression equation includes fewer schools, since a few schools lack
complete data. The schools analyzed have complete data for all variables.
The control variables include per cent faculty with only BA/BAS degrees,
student/computer ratios, per cent minority in school, mobility rates, per cent
free lunch eligible, per cent un-graded students, per cent federal revenues,
class size, which are entered as predictors along with school size.
"All things else equal", the relationship of school size with compounded
inefficiency is statistically significant at the .05 level of probability.
In fact, the level of probability is only .004 for a relationship this strong, given
the size of the obtained sample. School size in the past is closely linked to
the degree of inefficiency faced by high schools in the future, when one
looks at the combination of poor outcomes and high spending. Using other
indexes of inefficiency should produce similar conclusions.
Russell Harrison - Report on School Size and Education Outcomes - Page 93
SECTION 6
Summary of key variables and concepts
Section 6 summarizes the key variables used in this research, and the key concepts
used in regression analysis and hypothesis testing for these variables.
?Section 6A outlines the variables used to explain differences in test scores
in section 1.
?Section 6B outlines the variables used to explain the geographical
(spatial) concentration of violence within a district in section 2.
?Section 6C outlines the variables used to explain differences in
?compounded inefficiency? among high schools in section 3.
?Section 6D outlines the key concepts used in regression analysis and
hypothesis testing.
Russell Harrison - Report on School Size and Education Outcomes - Page 94
6A: Variables used to explain Differences in Test Scores in Section 1
96-97 Total Comparative Cost per Pupil [state index CCTOTY2]
Ccps9697
also dfin0066
99-00 Percent of Revenues from Federal [state index FED_Y5]
Fed9900
also dfin0027
96-97 Class size [state index CLSZ_Y3] ScFct029
96-97 Mobility rate [state index MOB_Y3] ScFct035
96-97 Student/Faculty Ratio 96-97 [state index STFA_Y3] ScFct041
96-97 % faculty with BA/BS [state index BA_Y3] ScFct072
96-97 Per cent African-American students pctblack
96-97 sum of students for 1996-1997 from NCES CCD totstu
Dependent Variables
Reading: % pass High school proficiency test in 1999-2000
[State index READ_Y6] HSPT029
Math: % pass High school proficiency test 1999-2000
[State index MATH_Y6] HSPT030
Writing: % pass High school proficiency test 1999-2000
[State index WRITE_Y6] HSPT031
Russell Harrison - Report on School Size and Education Outcomes - Page 95
6B: Variables used to explain the Geographical (Spatial) Concentration of Violence Within
A District in Section 2
SPSS index
Lagged School size: Mean of total students per regular school
during 1996-97 (from U.S. D.O.E. CCD files) meanstu1
District Size: 2001 Resident Enrollment for District ENROLL17
Race 2000: Per cent Asian students RACE0021
Race 2000: Per cent white students RACE0018
Poverty: 2000 Per cent eligible for free lunch or reduced price
lunch RACE0019
Spending: 2001-02 Comparative Cost Per Pupil VITALS04
Special Needs: 2001 Total Eligible for Special Education % (pct) ENROLL56
Intergovernmental: Local Taxes as proportion of 01-02 Revenue
Sources VITALS06
Class size: 2001 Student/ Teacher Ratio: 100 Students per
Teacher Ratio Fall 2001 (Certified Staff) VITALS11
The dependent variables measure the degree to which violent incidents within county
schools are concentrated within a given district
The proportion of total violence within
each county that occurs within a specific
district (%)
Index 1 uses the mean and Index 3 uses the
median to measure averages for a group of
districts
The ratio of Violent Incidents within Each
District versus Other Districts in the
County {%}
Index 2 uses the mean and index 4 uses the
median to measure average s for a group of
districts
All variables were measured using information provided by the U.S. and N.J.
Departments of Education.
Russell Harrison - Report on School Size and Education Outcomes - Page 96
6C: Variables used to explain differences in compounded inefficiency among NJ high schools in
Section 3
The independent variables measure school size, class size, and other independent
variables. Both expenditures and revenue sources are fiscal variables. The dependent
variables measure test scores, absenteeism, dropouts, as well as spending.
SPSS name
Source for each Variable
1996-97 % faculty with BA/BS ScFct072 [from state file BA_Y3]
1997-98 Student Computer Ratios ScFct110 [from State file stcomp_y4]
% minority in school for 1996-97 pctmin [from U.S. DOE CCD file for 96-
97]
Mobility rate for 1996-97 ScFct035 [from State file MOB_Y3]
% free lunch eligible (with NA=0) for 1996-97 pctpoor [from U.S. DOE CCD file for 96-
97]
% ungraded students [with missing = 0] for
1996-97 pctungrd [from U.S. DOE CCD file for 96-
97]
% federal revenues for 1999-00 fed9900 [from state file FED_Y5] - not
lagged
Class size - average for 1996-97 ScFct029 [from state file CLSZ_Y3]
School size = total enrollment/ sum of students
for 1996-1997 totstu [from U.S. DOE CCD file for 96-
97]
Total cost per pupil in 1999-2000 TCPS0001 [State index TOTCOSTY6]
Dropout Rate for 1999-2000 scfct026 [State index DROP_Y6]
Attendance Rate 1999-00 scfct020 [State index ATT_Y6]
Reading: % pass High school proficiency test in
1999-2000 HSPT029 [State index READ_Y6]
Math: % pass High school proficiency test 1999-
2000 HSPT030 [State index MATH_Y6]
Writing: % pass High school proficiency test
1999-2000 HSPT031 [State index WRITE_Y6]
In Section 3 each dependent variable is a composite index of compounded inefficiency. It
measures the degree to which each school suffers from low test-scores, low attendance-rates,
and high dropouts, in spite of high levels of spending per pupil.
Standardized z scores were computed for all NJ schools with available data, separately for each
variable. Then z scores for only those schools with complete information for all variables were
utilized to produce a composite index. In the composite index all six variables are equally
weighted, with + signs for fiscal burdens and dropout rates and negative signs for steady
attendance and favorable test scores.
All "cost" variables are based on official results for each school made public through NJ DOE
"report card" files.
Russell Harrison - Report on School Size and Education Outcomes - Page 97
SECTION 6D: Key Concepts
This section outlines the key concepts used in regression analysis and tests of null
hypotheses.
It is based on notes from classes by Dr. Russell S. Harrison in Quantitative Methods in
Social Science Research, Political Methodology, Evaluation Research, Research Methods
in Public Policy and Administration, and Education Policy.
Russell Harrison - Report on School Size and Education Outcomes - Page 98
ANOVA versus MRA
Concept
(abbreviation)
or acronym
Common
symbols
What the concept measures Meanings
Bivariate and
Multivariate
Relationships
Bivariate relationships measure the relationship between
one independent and one dependent variable.
Multivariate relationships take into account other possible
independent variables.
This research tests the relationships of school size with
various outcomes by measuring both bivariate and
multivariate relationships.
The goal is to see if a null hypothesis of no systematic
relationships can be systematically rejected.
In this research ANOVA is used to compare
means and evaluate the statistical
significance of bivariate relationships linking
school size to various outcomes.
MRA [multiple regression analysis] is used to
measure multivariate relationships (including
slopes that ?control? for spending, class size,
socio-economic traits of students, and other
?control? variables), and evaluate the
statistical significance of relationships.
Russell Harrison - Report on School Size and Education Outcomes - Page 99
Unstandarized Coefficients produced by SPSS MRA procedure [multiple regression analysis]
Slope
?b? in statistics
texts, or ?m? in
physics
B in SPSS
For multiple regression analysis, the slope measures the
linear relationship between an independent variable and a
dependent variable, ?taking into account? or ?controlling for?
the other independent variables in the equation.
The independent variables are predictors. For this analysis,
school size was typically measured several years prior to
each outcome, to emphasize that it was an ?exogenous?
predictor being used to explain variation in a given
?endogenous? dependent variable.
For a multiple regression equation, each slope measures
the relationship between an independent variable and the
residuals in a dependent variable not explained by the other
predictor variables.
The slope answers questions like these:
If I increase the independent variable by one
unit, by how many units will I increase or
decrease the dependent variable?
The slope is an unstandardized coefficient.
Therefore the value of the slope changes
depending on how you measure each
variable. Moreover, t he values for the slope
can range from -infinity to + infinity. Further,
you can easily deduce probable effects by
changing the independent variable by a given
multiple, such as 10 or 100 units.
The slope measures the ?elasticity? or
"productivity" of a relationship.
Intercept [slope
intercept]
?a? in statistics
texts, or ?b? in
physics
Intercept in
SPSS
Calculates the point at which a line will intercept the y-axis
by using a best-fit regression line plotted through the known
x values and y values.
It is used primarily as a means to compute predicted values
for a dependent variable.
What is the value of the dependent variable if
the value of each independent variable is
zero?
The answer can have any positive or negative
value, which may or may not exist in a given
universe of observed cases.
Standard error
of slope
Std Err in
SPSS
Returns the standard error of the predicted y-value for each
X in a regression equation. Though unstandardized, it is
used to produce the standardized t ratio.
The standard error is determined by the
average difference between the predicted and
observed values of the dependent variables,
weighted by extreme differences between the
predicted and observed values.
The answer is always a positive value, since it
is equivalent to the standard deviation of
deviations about the regression equation.
Russell Harrison - Report on School Size and Education Outcomes - Page 100
Standardized MRA coefficients
Beta
?B? in
statistics texts
Beta in SPSS
Returns the value of a slope assuming that all variables are
measured in z-scores or at least standard deviation units.
The Beta answers questions like these:
If I increase the independent variable by one
standardized unit, by how many units will I
increase the dependent variable?
It is a standardized coefficient that typically
ranges in value from ?1 to +1. Any more
extreme scores often indicate a multi-co
linearity problem.
t-coefficient or tratio
?t? in SPSS
Measures the ratio of a slope to its standard error, which
indicates the relative importance of a variable assuming
standardized measurement procedures
This coefficient is commonly used to measure
the statistical significance of a relationship.
Significant relationships have a large t-ratio
and a large sample size. Thus the same
relationship for a smaller sample may not
produce the same ?significance? level.
Different types of t-coefficients are used in
regression analysis, ANOVA or comparison of
means, etc.
R-squared
coefficient,
which typically
equals the
square of the R
coefficient
R**2
In SPSS
The square of the R coefficient for a multiple regression
equation
Sometimes called the coefficient of determination.
The adjusted R-squared takes into account the number of
independent variables relative to the sample size. It
generally measures the degree to which a set of variables
explains outcomes in a given dependent variable, or the
quality of the overall regression equation.
This coefficient answers:
How much of the variation in the dependent
variable is explained by the independent
variable (expressed as a proportion)?
The answer will have a value of .00 to 1.00.
Russell Harrison - Report on School Size and Education Outcomes - Page 101
Linking SPSS ?Sig? Coefficients to formal tests of ?null? hypotheses
Significance
level
Labeled
simply as ?sig?
in SPSS
= the statistical significance for a given slope, or difference
in means, R**2, etc.
The observed value for the SPSS ?sig? coefficient will have
a range of values from .00 to 1.00. The smaller the
observed value, the more important or ?statistically
significant? the observed relationship, and the greater the
confidence one has in rejecting the ?null hypothesis?. By
tradition in exploratory social science research, the critical
threshold is .05.
The ?sig? coefficient answers questions like
these: How much error should I expect if I
reject the null hypothesis?
If the error is less than .05 or 5%, you can
reject the null hypothesis at the .05 level of
probability, following the typical norms in the
social sciences for exploratory ?needs
assessment? research as part of a formal
strategic planning process.
For large samples and follow-up research, the
criterion for the ?level of probability? threshold
may be set at .01 or even .001 to reject the
null hypothesis.
Null hypothesis Ho: = an assumption or prediction that the relationship between
two variables is null, which the researcher typically wishes
to disprove
= in MRA an assumption that the dependent variable is not
a linear function of the independent variable, and that
variation in the dependent variable does not systematically
vary as a ?monotonic? function of the independent variable
note: often ?tipping point? analysis is used to identify
specific levels of the independent variable above and below
which the average scores of the dependent variable
dramatically vary
ANOVA measures the degree to which differences or
variation in the dependent variable are greater between
categories of the independent variable than within
categories of the independent variable
This preliminary needs-assessment research
tested the empirical relationships between
school size and three outcomes, for given
samples. The task was to see if the observed
?sig? coefficient or ?significance? level were
small enough to reject the null hypothesis with
a reasonable level of confidence that the
same conclusions would be drawn by future
research using analogous samples. This
could be done, using the standard threshold
for statistical significance. However, further
research is needed to confirm relationships in
different samples, such as those for
elementary and middle schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 102
SECTION 7 ? Key Readings on Methods
This section summarizes key readings about optimal methods to
research size outcomes.
In addition to author, title, and source, a key feature of each study is
highlighted.
Russell Harrison - Report on School Size and Education Outcomes - Page 103
7A: How best to utilize MRA
Jay Greene
The Education
Freedom Index
[September
2000]
The
Manhattan
Institute for
Policy
Research
Civic
Report 14
Illustrates the use of multiple regression
analysis [MRA] to link institutional structures
with education outcomes. His ?control?
variables include spending and class size, as
well as the poverty and race of students. His
?freedom index? and his dependent variables
illustrate the use of composite indexes in MRA.
Jay Greene 2001 Education
Freedom Index
[January 2002]
The
Manhattan
Institute for
Policy
Research
Civic
Report 24
Further illustrates the use of multiple regression
analysis to link institutional structures with
education outcomes. His ?ceteris paribus?
controls again include spending per student,
class size, poverty, and race of students.
Such research provides ample precedent for
similar controls in the present study.
Herbert J.
Walberg
& Fowler,
W.
Expenditure and
size efficiencies
of public school
districts.
(1987).
.
Educational
Researcher,
16(7), 5-13.
Illustrates how ?residuals? from multiple
regression analysis can be used as an index of
educational efficiency, and the need to model
those residuals as a function of district size. By
analogy, one can perform the same task for
school size. See section 4.
Herbert J.
Walberg.
District size and
student
learning.
(1989).
Education
and Urban
Society,
21(2), 154-
163
Shows how to use regression techniques to
measure relationships. Illustrates the impact of
district size on academic outcomes. Provides
clear precedent for exploring another index of
institutional size, namely school size.
Herbert J.
Walberg,
Losing Local
Control of
Education: Cost
and Quality
Implications
(1993)
Heartland
Policy
Study, The
Heartland
Institute,
November
22, 1993.
Again uses regression analysis, this time with
controls for spending and minority population,
though his data refer to states. Provides clear
precedent for applying similar methods to
analyze individual districts or schools.
Robert L.
Hampel
?The Long
Road to Small
Schools? (2002)
Education
Digest,
April 2002,
Vol 67 Issue
8, 15-21, via
ESBCO
Stresses the need to study multiple outcomes
from school size. Traditional proponents of
large schools in prior eras believed they offered
multiple advantages. To refute traditional
myths, empirical research must document the
multiple advantages of small schools, and the
multiple disadvantages of large schools, for the
present era.
Russell Harrison - Report on School Size and Education Outcomes - Page 104
7B: The Need to Measure Lagged relationships
David
Mayston,
University
of York
Tackling the
Endogeneity
Problem When
Estimating the
Relationship
Between School
Spending and
Pupil Outcomes
(2002)
British
Department
for
Education,
Research
Brief No.
328,
January
2002, ISBN
1 84185 667
3
Stresses the take to take into account potential
endogenous relationships when measuring
linkages among school traits like spending,
class size, school size, and educational
outcomes.
The Harrison research uses lagged relationships
to minimize feedback problems, which offer
many advantages over traditional regression
procedures where predictors and dependent
variables are measured in the same year.
Peter
Blatchford,
Clare
Martin, Viv
Moriarty,
Paul
Bassettt,
and Harvey
Goldstein,
Institute of
Education,
University
of London
Pupil Adult
Ratio
Differences and
Educational
Progress over
Reception and
Key Stage 2
(2002)
British
Department
for
Education,
Research
Brief No.
335, May
2002, ISBN
1 84186 702
5
Emphasizes that class size may have little
impact on school children?s educational
progress, versus other constraints on the
educational production process.
Also emphasizes the need to look at educational
impacts over time.
The Harrison research uses lagged relationship
to take into account educational impacts over
time. The new research shows that school size
has become far more important than class size
as a determinant of educational outcomes in
New Jersey, ?ceteris paribus? - all things else
equal.
Russell Harrison - Report on School Size and Education Outcomes - Page 105
7C: The need to go beyond Money and Class size
An increasing number of scholars have begun to question the traditional public school mantras
that money and class size are all that matter for education, at least on a macro-level of policy
reform. Opponents of the traditional views include various ?institutionalists? like Erik
Hanushek, Caroline Hoxby, John Chubb, Terry Moe, Paul Peterson, Herbert J. Walberg,
Chester Finn, Jr., even though they have not yet directly addressed the issue of school size.
E. A.
Hanushek
(a) ?The Impact
of Differential
Expenditures on
School
Performance?
(1986)
Educational
Researcher,
18 (4), 45-
65.
E. A.
Hanushek
(b) ?The
Economics of
Schooling:
Production and
Efficiency in
Public Schools?
(1986)
Journal of
Economic
Literature
1147
In 1986 Erik Hanushek introduced a long line
of meta-analyses that document the declining
importance of both class size and finances in
explaining educational outcomes. Since then
other studies have documented the importance
of other variables connected to the size of
districts or schools. These include the types of
cooperative decision-making, parental
inclusion, ?connectedness?, ?trust?,
?educational restructuring?, and ?professional
learning communities? possible in smaller
schools.
Ronald
Fisher
State and Local
Public Finance
(1988)
Glenview
Illinois:
Scott
Foresman &
Company,
Ch. 18,
?Education?
The traditional point of view on the importance
of money in ?educational production functions?
Helen Pate-
Bain et al.
?Class Size
Does Make a
Difference?
(1996)
In Jack R. Van
Der Silk,
Politics in the
American
States and
Communities,
A
Contemporary
Reader, pp.
254-259
The traditional point of view on the importance
of class size for student academic performance
Russell Harrison - Report on School Size and Education Outcomes - Page 106
7D: Traditional Perspectives And Empirical Contradictions on
Large Scale Educational Service Delivery Structures
Ernest
Reock
The Cost
Impact of
School District
Creation and
Consolidation
in New Jersey.
(1995)
Occasional
Paper Series
# 3, Center
for
Government
Services and
Public
Affairs
Research
Institute of
New Jersey,
Inc., March
1995
Reock has been a major advocate for
centralization and large-scale service delivery
units. The 1995 report remains a primary
reference for advocates of district mergers in
New Jersey. He presents data that purport to
prove that ?fragmentation? increases costs.
In fact, a reanalysis of the data reported reveals
that the longer a district has been merged, the
greater the growth in costs over time. The
evidence actually confirms that adverse fiscal
effects emerge over time from attempts to
merge schools with students from different
communities. Where schools serving different
communities are merged into one big
administrative structure, costs escalate.
In any event, his evidence refers to districts, not
to schools per se. Nor does he actually measure
the size of the merged districts he studies. He
simply reports when they were created out of
their feeder districts. Thus his research as a
whole most emphatically does not document the
fiscal superiority of big schools, if one
correlates the duration of mergers with growth
in costs over time.
Russell Harrison - Report on School Size and Education Outcomes - Page 107
James B.
Conant
The
American
High School
Today
(1959)
New
York:
McGraw
Hill
The 1959 Conant study is one of the most widely
cited studies that advocate the merits of large high
schools. Conant presents a survey of 22 high schools
to bolster his claim that bigger schools are better,
especially for gifted and talented students. Even
ignoring his biases in who should benefit from school
reform, his survey does not support his thesis that big
schools are best.
(1) A reanalysis of his data reveals a negative
correlation between school size and the proportion of
students who are able to participate in the gifted and
talented classes. The larger schools had a smaller per
cent of their student bodies involved in gifted and
talented classes, even though they had more students
overall. This confirms that then - as well as now, big
schools hurt the percent who benefit from what the
school has to offer ? especially for extra-curricular
activities. They may have more specialized
resources, but a smaller share of students benefits
from them.
(2) Worse, the reanalysis shows a positive correlation
between school size and the proportion of students
who fail to complete the basic number of courses in
English and Social Studies that he recommends.
Thus the students at the bottom are especially hurt,
who fail to complete even the minimum core of the
available courses.
(3) Worst, the survey reveals that school size is
positively correlated with various indices of chaos
and conflict in the school climate. Larger schools
have school climates marked by excessive chaos and
conflict. Both teachers and students suffer from the
dysfunctional social climate that is exaggerated in the
larger schools, both then and now.
Russell Harrison - Report on School Size and Education Outcomes - Page 108
SECTION 8 ? Key Research
Section 8 summarizes readings that clarify key research on school size
outcomes and options for implementation of small school policies.
Russell Harrison - Report on School Size and Education Outcomes - Page 109
8A: Inventories of research on the multiple positive outcomes
from small school learning communities ?
Perspectives on School Size Outcomes and Implementation Options Section
Author Title Source Feature
Kathleen
Cotton
School Size,
School
Climate, and
Student
Performance
(1996)
Close-up #20.
Portland
Oregon,
Northwest
Regional
Educational
Laboratory.
Provides an extremely comprehensive survey of
positive outcomes from small schools, and the
different research studies that document or at
least discuss each type of outcome.
Kathleen
Cotton
Affective
and Social
Benefits of
Small-Scale
Schooling
(2000)
ERIC,
Clearinghouse
on Rural
Education and
Small Schools
Points out the multiple psychological benefits of
small schools, including positive morale and
sense of personal efficacy among teachers, a
sense of belonging and social bonding among
students, a greater sense of self-esteem and
positive evaluations towards the school climate
by both teachers and students.
Outlines the social benefits of small schools
which include less social disruption and
behavioral problems, better attendance and fewer
dropouts, a greater increase in the percent of
students who participate in extra-curricular and
advanced academic programs, unlike large
schools where only a small proportion of students
are given access.
Mary
Anne
Raywid
Downsizing
Schools in
Big Cities
(1996)
ERIC Digest,
the ERIC
Clearinghouse
on Urban
Education
Points out the multiple benefits of small schools
for a wide range of stake-holders ? teachers,
students, and parents
Mary
Anne
Raywid
Current
Literature on
Small
Schools
(1999)
ERIC Digest,
the ERIC
Clearinghouse
on Rural
Education and
Small Schools,
January 1999
Points out that both quantitative studies and case
studies document superior outcomes for small
schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 110
8B: Other syntheses of favorable outcomes from
Small School Learning Communities -
Perspectives on School Size Outcomes and Implementation Options
Ayers, William, Bracey, Gerald, and Smith, Greg. The Ultimate Education Reform? Make Schools
Smaller [University of Wisconsin-Milwaukee, School of Education, Center for Education Research,
Analysis, and Innovation, PO Box 413, Milwaukee WI 53201 SDIP Education Policy Project, CERAI-00-
35; 12/14/2000]
Cotton, Kathleen. School Size, School Climate, and Student Performance. Portland, OR: NW Regional
Lab. 1997
Raywid, Mary Ann, ?Small Schools: A Reform That Works,? Educational Leadership, 55:4
December/January, 1997/?98.
Fowler, W. J., Jr. "School Size and Student Outcomes." Advances in Educational Productivity 5 (1995):
3-26.
Sergiovanni, T. J. Organizations or Communities? Changing the Metaphor Changes the Theory. Paper
presented at the Annual Meeting of the American Educational Research Association, Atlanta, GA, April
1993 (ED 376 008).
Gregory, T. "Small Is Too Big: Achieving a Critical Anti-Mass in the High School." In Source Book on
School and District Size, Cost, and Quality. Minneapolis, MN: Minnesota University, Hubert H.
Humphrey Institute of Public Affairs; Oak Brook, IL: North Central Regional Educational Laboratory,
1992, 1-31 (ED 361 159).
Stockard, J., and Mayberry, M. "Resources and School and Classroom Size." Chapter 3 in Effective
Educational Environments. Newbury Park, CA: Corwin Press, Inc., 1992, 40-58.
Smith, D. T., and DeYoung, A. J. "Big School vs. Small School: Conceptual, Empirical, and Political
Perspectives on the Re-emerging Debate." Journal of Rural and Small Schools (Winter 1988): 2-11
Barker, B. O. The Advantages of Small Schools. ERIC Digest. Las Cruces, NM: ERIC Clearinghouse
on Rural Education and Small Schools, February 1986 (ED 265 988).
Cohen, B. P. The Effects of Crowding on Human Behavior and Student Achievement in Secondary
Schools. Philadelphia, PA: Philadelphia School District, Office of Curriculum and Instruction, 1975 (ED
188 279).
Russell Harrison - Report on School Size and Education Outcomes - Page 111
8C: Specific Benefits of
the Small School Learning Community
involving test scores, violence, and/or
?compounded inefficiency? costs
8C1: Raise student achievement
[including minority or low-income students]
Howley, Craig, Bickel, R. The Matthew Project: National Report. ERIC: ED433174. 1999 1999
Howley, C. "Literature Review." In Sizing up Schooling: A West Virginia Analysis and
Critique. Unpublished Doctoral Dissertation, West Virginia University, Morgantown, WV,
1996.
1996
Howley, C. B. "The Matthew Principle: A West Virginia Replication?" Education Policy
Analysis Archives 3/18 (November 15, 1995): 1-25. Electronic journal:
http://epaa.asu.edu/epaa/v3n18.html
1995
Howley, C. The Academic Effectiveness of Small-Scale Schooling (An Update). ERIC
Digest. Charleston, WV: Clearinghouse on Rural Education and Small Schools, June
1994 (ED 372 897).
1994
Huang, G., and Howley, C. "Mitigating Disadvantage: Effects of Small-Scale Schooling on
Student Achievement in Alaska." Journal of Research in Rural Education 9/3 (Winter
1993): 137-149.
1993
Fowler, W. J., Jr., and Walberg, H. J. "School Size, Characteristics, and Outcomes."
Educational Evaluation and Policy Analysis 13/2 (Summer 1991): 189-202. 1991
Friedkin, N. and Necochea, J. ?School System Size and Performance: A Contingency
Perspective,? Educational Evaluation and Policy Analysis, Vol 10, No. 3, 1988, pp. 237-
249.
1988
Miller, J. W.; Ellsworth, R.; and Howell, J. "Public Elementary Schools Which Deviate from
the Traditional SES-Achievement Relationship." Educational Research Quarterly 10/3
(1986): 31-50.
1986
8C2: Reduce incidents of violent and disruptive behavior
Bailey, J. ?The Case for Small Schools,? Center for Rural Affairs Monthly Newsletter,
2000. 2000
Berreth, D. ?Supporting Schools as True Communities of Character,? Testimony before
the House Subcommittee on Early Childhood, Youth, and Families, 2000. 2000
Rossi, R. and Daugherty, S. ?How Safe are the Public Schools: What Do Teachers Say??
Washington, D.C.: National Center for Education Statistics, 1996 1996
Gottfredson, D. C. School Size and School Disorder. Baltimore, MD: Center for Social
Organization of Schools, Johns Hopkins University, July 1985 (ED 261 456). 1985
Russell Harrison - Report on School Size and Education Outcomes - Page 112
8C3: Decrease absenteeism and dropouts,
increase graduation rates cost-effectively
Farber, P. ?Small Schools Work Best for Disadvantaged Students,? Harvard Education
Letter, March/April, 1998. 1998
Fetler, M. "School Dropout Rates, Academic Performance, Size, and Poverty: Correlates
of Educational Reform." Educational Evaluation and Policy Analysis 11/2 (Summer 1989):
109-116.
1989
Jewell, R. S. "School and School District Size Relationships: Costs, Results, Minorities,
and Private School Enrollments." Education and Urban Society 21/2 (February 1989):
140-153.
1989
Toenjes, L. A. Dropout Rates in Texas School Districts: Influences of School Size and
Ethnic Group. Austin, TX: Texas Center for Educational Research, August 1989 (ED 324
783).
1989
Pittman, R. B., and Haughwout, P. "Influence of High School Size on Dropout Rate."
Educational Evaluation and Policy Analysis 9/4 (Winter 1987): 337-343. 1987
Rogers, R. G. "Is Bigger Better? Fact or Fad Concerning School District Organization."
ERS Spectrum 5/4 (Fall 1987): 36-39. 1987
Lindsay, P. "The Effect of High School Size on Student Participation, Satisfaction, and
Attendance." Educational Evaluation and Policy Analysis 4/1 (Spring 1982): 57-65. 1982
Steifel, L., Berne, R., Iatarola, P., Fruchter, N. ?High School Size: Effects on Budgets and
Performance in New York City,? Educational Evaluation and Policy Analysis, Vol. 22, No.
1, Spring, 2000, pp. 22-39. See
http://www.uwm.edu/Dept/CERAI/documents/archives/00/cerai-00-35.htm - _ednref7.
2000
Nachtigal, P. "Remapping the Terrain: School Size, Cost, and Quality." In Source Book on
School and District Size, Cost, and Quality. Minneapolis, MN: Minnesota University,
Hubert H. Humphrey Institute of Public Affairs; Oak Brook, IL: North Central Regional
Educational Laboratory, 1992, 52-71 (ED 361 161).
1992
Russell Harrison - Report on School Size and Education Outcomes - Page 113
8D: Perspectives on how to implement
Self-sustaining Small School Learning Communities ?
Perspectives on School Size Outcomes and Implementation Options
Author Title Source Feature
Mary
Anne
Raywid
Taking Stock:
The
Movement to
Create Mini-
Schools,
Schools-
Within-
Schools, and
Other Small
Schools
(1995)
ERIC,
Clearinghouse
for Urban
Education,
Columbia
University:
New York
The problems that plague symbolic attempts to
achieve the benefits of small schools without
actually establishing autonomous facilities and
administrative structures for each school that
permit a maximum of site-based decision-making.
Also an excellent overview of the early research
on the multiple benefits of autonomous small
schools.
Kathleen
Cotton
School Size,
School
Climate, and
Student
Performance
(1996)
Close-up #20.
Portland
Oregon,
Northwest
Regional
Educational
Laboratory,
1996.
Provides a bibliography that lists key research on
?alternative schools?, SWAS/ schools within a
school, and other structures that combine a limited
range of student enrollment with the varied
positive features of the small school learning
community.
The list of annotated articles can be obtained from
the American Association of School
Administrators, 1801 North Moore Street,
Arlington, VA 22209-1813. It includes specific
studies dealing with SWAS and ?alternative
schools?, some of which feature ?academy? style
specializations.
Patricia
A.
Wasley
and
Richard
J. Lear
?Small
Schools, Real
Gains?
(2001)
Educational
Leadership,
22-27.
Points out the multiple positive features of the
small school learning community, and conditions
that impede the successful implementation of such
a community.
These include legislative and judicial mandates
that favor larger schools and centralize operations,
including extra aid for larger schools, larger
districts, and pro-consolidation ?research?
projects, plus attempts at the state and district
level that force small schools to act like large
schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 114
SECTION 9 - Implementation
Section 9 outlines future research priorities for the New Jersey
Commission on Business Efficiency in the Public Schools with regard to
specific policies to implement small school learning communities:
Future Research Should Explore A Range Of Policies For Implementing a Small
School Learning Community, ranging from incremental to radical.
A. Incremental reforms include the SWAS/ Schools within Schools/
approach. However, serious caveats must be imposed on its probability of
success as a self-sustaining policy.
B. Incremental reforms include a close look at Focus schools or ?Specialism?
schools like those used in England to overcome the disadvantages of oversized
schools.
C. Incremental reforms include a revision in state mandates for consolidation
studies. Future studies should measure and document the growth in
adverse educational outcomes that occur over time in districts with larger
schools.
D. Moderate reforms include a policy to facilitate the permission and
certification process for small Charter Schools or other Alternate schools
in ?high risk? districts subject to federal ?choice? guarantees. The process
should be simplified in districts where student performance is poor,
absenteeism and dropouts are high, and school size surpasses critical
tipping points. Moreover, small new schools should be given extra time to
document their successes, since school size produces positive benefits that
extend over time.
E. A radical reform would require courts to take into account the possibility
that school size is now a larger source of inefficiency and inequality in
school operations than is class size, much less spending per student.
Courts would be mandated to consider the implications of new research
that shows a negative correlation between school size and the ability of
school officials to operate a ?thorough and efficient? system of education.
Schools are not thorough where learning is minimized, and absenteeism
and dropouts are maximized. Schools are not efficient, where money is
spent with declining marginal returns, and where test scores fall far short
of what one would expect from spending, class size, school resources,
student ethnicity and poverty, and other factors.
F. Another radical reform would allow districts to trade-off smaller schools
for smaller classes. Research is needed to document that the same per cent
change in school size and class size would improve performance and cut
costs, assuming that the per cent reduction in school size would match the
per cent increase in class size.
Russell Harrison - Report on School Size and Education Outcomes - Page 115
Section 9A, 9B, 9C
Future research should explore incremental reforms as one strategy for Implementing The
Small School Learning Community
9A: Incremental Reforms include Schools within Schools or SWAS structures.
?Research should clarify the need for implementation rules for Schools
within Schools and similar policies that avoid common implementation
errors outlined by Tom Gregory and others. See, among others:
o Tom Gregory, ?Breaking Up Large High Schools: Five Common
(and Understandable) Errors of Execution?, ERIC Digest EDO-RC-
01-6, December 2001
o Tom Gregory, ?School Reform and the No-Man?s-Land of High
School Size?, unpublished paper provided by author at University of
Indiana, December 2000
?Research should clarify the dangers outlined by Kathleen Cotton, Mary
Ann Raywid, and others about the limited payoffs of plans that do not
guarantee independent physical facilities, autonomous administration, and
relief from mandates that disproportionately impose undue burdens on
smaller schools.
9B: Incremental Reforms include support for Focus Schools or ?Specialism? schools like
those used in England, or various ?Academy? or ?Alternate School? programs in the
United States.
?To reduce the adverse effects of large schools in England, Focus/
Specialist Schools have been established, which now house a large
proportion of all secondary students in the country.
o The state legislature should fund new research on the effects of
?focus? schools on education outcomes over time. To what extent can
focus/specialist schools minimize the adverse effects of school size?
o The research should not be limited to states like New Jersey where
most such schools are relatively new, and the number of schools is
relatively small. The research should look at evidence for settings like
England, where the practice has had more time to produce effects over
time, and where tens of thousands of students attend such schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 116
9C: Another incremental reform would require the legislature to revise mandates for
state funded ?consolidation? studies, or replace them with a less biased approach to needs
assessment
?The ?needs assessment? must make use of environmental scanning
techniques to document the effects of larger districts and schools over
time, and not assume that all benefits will be beneficial.
?The ?needs assessment? must measure the extent to which district
consolidation projects result in escalating costs over time
?All consolidation needs assessment must measure and document the
growth in adverse educational outcomes that occur over time in districts
with larger schools, including lower test scores, increased violence, and
greater inefficiency
?The ?needs assessment? must identify those tipping points which are
associated with significantly higher levels, and reject any plans that result
in school enrollments that exceed those caps.
Russell Harrison - Report on School Size and Education Outcomes - Page 117
9D: A moderate reform would be to ease the task of creating charter schools and
alternate schools in districts with over-sized and under-performing schools.
?New federal budget guidelines seek to implement the basic premises of the No
Child Left Behind philosophy. This includes a notion that under-performing
children in disadvantaged districts should be given a wider array of ?choice?
options ? so their parents can help them choose an alternative school more suited
to their needs that would help them realize their potential. Advocates of
?competition? support this notion. They claim that choice and competition among
schools improve educational outcomes, and especially the productivity and
efficiency of the educational process.
?How would an expansion of small schools maximize the benefits alleged by the
advocates of choice and competition? New Jersey officials could mandate that all
at risk children be given the right to transfer to a small school, where enrollments
are controlled to maximize efficiency and productivity in learning, and minimize
social chaos.
?Research should also explore the validity of new rules to facilitate the creation of
new Charter Schools or Alternate Schools within any district burdened with oversized
schools and under-performing children. Moreover, these new schools
should be given a track record of at least three years of operation before
measuring outcomes, since the benefits of small school size tend to accrue over
time. Finally, research should explore the degree to which small charter schools
produce the same positive payoffs as small public schools in general. In
particular, research should look at value added, or what happens to test scores
over time, as well as what happens to social behavior and attitudes within the
school.
?If traditional public schools refuse to downsize, then ?adequacy? mandates should
be imposed which facilitates the creation of and transfer to competing small
schools.
Russell Harrison - Report on School Size and Education Outcomes - Page 118
9E, 9F: Radical reforms
9E: One radical reform would place caps or ceilings on future school litigation, to ensure
judicial restraint.
?The legislature should stipulate that no state funding will ensure from
litigation unless the case decision is based on scientific Brandeis Briefs
that take into account the actual determinants of education outcomes
today, rather than the myth that money and smaller classes are the ultimate
cure all for all problems facing schools, and that consolidation is a major
source of efficiency in public school education production functions
?Legislative and judicial mandates should stipulate that courts must
consider the fact that money and class size are no longer as important as
school size as a determinant of outcomes, and that the traditional
assumption that money and smaller classes are a cure all may be a major
cause of inflated costs for state and local tax payers.
?Legislative and judicial mandates should stipulate that courts must
consider the fact that the top decile poverty (poorest) districts in New
Jersey already receive and spend more money from state and local
sources, and especially from state sources, than do the bottom decile
(richest) districts. They probably also receive much more federal aid,
especially as a percent of their locally generated revenues. Research is
needed to examine the degree to which dependence on outside funding is
associated with a loss of local control and increased inefficiency in
education, versus small schools that can increase local control and
decrease inefficiency. Simply changing sources of revenues to restrict
local contributions may not work as well as simply changing school size.
9F: Balancing tradeoffs between school size and class size
Another radical reform would be to take into account the possibility that class
size and school size reforms produce quite different ratios of costs to benefits. Smaller
classes have little ability to maximize positive academic outcomes. However, they do
maximize spending per student. In short, a small class policy maximizes costs relative to
benefits.
In contrast, smaller schools have a major ability to maximize positive academic
outcomes. However, they have little or no impact on current spending per student, and
may increasingly cut capital spending per student. Overall, small school policies
maximize benefits relative to costs.
Consequently, policies that cut school size at the same rate than class size is freed
will result in major costs savings plus improved academic outcomes.
Thus a policy that deserves further review is the following. Legislation should
provide districts with prerogatives to trade-off smaller schools for larger classes, if they
wish to minimize costs and maximize academic outcomes. Simultaneously, they should
be freed from arbitrary state mandates for staffing and curriculum delivery options that
impose disproportionate fiscal costs on small schools, and inflate staff/student ratios.
Russell Harrison - Report on School Size and Education Outcomes - Page 119
SECTION 10 - FOLLOWUP RESEARCH
This section outlines future research priorities for The New Jersey Commission
On Business Efficiency In The Public Schools. It lists a range of specific studies that are
needed to clarify how smaller schools can improve the efficiency and equity of education
in New Jersey.
Russell Harrison - Report on School Size and Education Outcomes - Page 120
Summary of Needed Follow-up Research to the present study
Dependent Variable
or Outcome
Year 1 of overall
project
Specific topics for research follow-up
Test Scores Rejected null
hypothesis for
HSPT scores (for
high school
students)
Test null hypothesis
for ESPA and
GEPA scores
(elementary and
middle schools)
Include lower
grades in analysis.
Violence Rejected null
hypothesis for
concentration of
violence in High
School districts
Test null hypothesis
for elementary and
middle schools
Measure violence as
well as non-violent
crimes in lower
grades as a function
of school size.
Include lower
grades in analysis.
Test null hypothesis
using data for
individual schools
Control for the DFG
of each school to
show that school
size does not simply
escalate violence in
the poorest districts
but also in middle
class districts
Inefficiency Rejected null
hypothesis for
compounded
inefficiency which
measures the
combination of high
spending and poor
results
Test null hypothesis
for elementary and
middle schools.
Include lower
grades in analysis.
Use two-stage
residual analysis to
focus on separate
components of the
inefficiency index.
.
Create a new index
of ?efficiency? that
isolates the effects
of school size on
each component of
compounded
inefficiency
separately.
Russell Harrison - Report on School Size and Education Outcomes - Page 121
Specific
outcome
Year 1 Needed Research Follow-up
Examine causes and consequences of dropouts
and absenteeism separately.
Test null hypotheses for dropouts and
absenteeism separately, as well as how school
size and absenteeism combine to shape dropouts
Test null hypotheses separately for high schools
and for elementary and middle schools ?
Examine results for all schools collectively.
Utilize the Jay Greene index of de facto dropouts
to see how many more dropouts NJ schools
suffer than those reported using the de jure
records
Measure specific indexes of dropouts and
absenteeism and evaluate how much school size
affects dropouts and absenteeism over a four
year period
Dropouts and
Absenteeism
as key indices
of a
dysfunctional
?school
climate?
Only examined as
part of a larger
composite index
Develop ?residual? indices of success in dealing
with problems of dropouts and absenteeism,
relative to spending, class size, and the social
traits of students.
Confirm that school size reduces how efficiently
schools deal with problems of dropouts and
absenteeism, relative to resources expended and
the types of students served.
Russell Harrison - Report on School Size and Education Outcomes - Page 122
Specific
outcome
Year 1 Needed Research Follow-up
Measure effects of school size on municipal
overburden and tax rates, in part due to effects
of school size on dropouts, youth crime, female
heads of households, and other culture of poverty
problems both in and out of school.
Document that municipalities served by districts
with larger schools develop higher tax rates over
time.
Measure effect of school size on declining
house values.
Document effects of school size on flight of
middle class from communities with over-sized
schools and subsequent loss of school quality in
over-sized schools.
Document how declining house values mean
declining ratables, which drive up tax rates, in
conjunction with increasing social problems
Measure effects of school size on combination of
construction, maintenance, transportation costs,
land acquisition costs, suburban sprawl, and
other major indirect costs of big school design
principles
Show that nationwide big schools are no longer
as cost efficient as small schools when one takes
into account:
?Cost of land acquisition and loss of open
space,
?Loss of options to recycle and refurbish
preexistent facilities possible with
smaller schools, as well as modular
options to mega-school boxes,
?The benefits of small schools as part of
the ?new urbanism? approach to
neighborhood planning and architecture.
Fiscal costs Only examined as
part of a larger
composite index
The index only
included current
spending on certain
specific budget
items.
Develop a computer simulation to document
total fiscal costs over time to federal, state, and
local government of dealing with dropouts
produced by large schools, in addition to the loss
in foregone income by those dropouts. Include
welfare, corrections, judicial, and public
health costs.
Russell Harrison - Report on School Size and Education Outcomes - Page 123
Specific
outcome
Year 1 Needed Research Follow-up
Reduction in
ability of
traditional
inputs to
maximize
academic
outputs,
especially
spending per
student and
class size.
Not assigned for
this study
Document that the growing size of schools reduces
the marginal returns from traditional educational
inputs like expenditures, class size, teacher
training, computer resources, etc., so that now
school size is far more important in shaping
academic outcomes than any one of these inputs.
Document that school size is over 100% more
important than class size in shaping test scores.
Document that school size is over 100% more
important than spending per student in shaping test
scores.
De facto
discrimination
and bias in
academic
achievement
Not assigned for
this study
Document that school size exaggerates the adverse
effects of poverty and minority status on test score
achievements in a way that exaggerates inequality
in learning.
Discuss the constitutional law implications of this
finding.
De facto
segregation due
to the isolation
and
concentration
of poverty
students in
declining
schools
Not assigned for
this study
Document that school size is correlated with the
loss of middle class students over time, and the
subsequent isolation and concentration of poverty
students into academic ghettoes.
Discuss the implications for segregation laws and
standards affecting NJ schools..
Overall student
crime versus
violence per se
Not assigned for
this study
Test a null hypothesis linking school size to other
varieties of student crime besides violent incidents
per se.
Document that school size exaggerates the degree
to which community problems like drug use
escalate into violence, and that school size
therefore independently increases violence separate
and distinct from catalysts like drug use
Explore effects of school size on vandalism at
various levels of schooling.
Russell Harrison - Report on School Size and Education Outcomes - Page 124
Specific
outcome
Year 1 Needed Research Follow-up
Implementation
methods for
Small School
Learning
Communities
Empirical
research on
implementation
options was not
assigned for this
study
Incremental reforms
Document the degree to which ?focus? schools or
?choice? schools in New Jersey may ? or may not -
maximize the advantages of smallness. [Focus
schools include academy schools or ?specialism?
schools. In turn, focus schools are often the focus
of SWAS/ school within a school structures.]
Document the extent to which the benefits of
?focus? schools in New Jersey are obscured due to
their disproportionate recruitment of minority and
poverty students.
Examine the degree to which ?focus? schools in
other states and England maximize the advantages
of smallness. Test a null hypothesis linking
?academy? structures with higher test scores and
fewer social problems like absenteeism for
England.
Document the extent which ?focus? schools or
?choice? schools in N.J. maximize test scores -
independently of their size and resources which
differ dramatically from other schools..
Moderate reforms
Document the inadequacies of present state
incentives for local districts to consider the merits
of consolidation, regionalization, and centralization
of administration.
Document that whatever the effects of district size
on academic costs and benefits, school size has an
independent impact on academic outcomes,
including absenteeism, dropouts, and overall school
crime and violence.
Radical Reforms
Develop a computer similar to document how
many hundreds of millions of dollars would be
saved, and how many thousands of incidents of
violence, physical conflicts, fear, and intimidation
would be eliminated, from the implementation of a
tradeoff policy that would cut school size by 10%
while allowing class size to rise by the same
proportion over a ten year period.
Russell Harrison - Report on School Size and Education Outcomes - Page 125
Radical Reforms
Measure the degree to which the traditional
premises of ?the public school finance reform
litigation crusade? have become correlated with an
increase in costs that far outweighs any increase in
academic benefits.
Test a null hypothesis linking traditional litigation
outcomes from state supreme court decisions to
compounded inefficiency outcomes.
Show that an excessive emphasis on equity goals in
court litigation versus efficiency litigations means
that court rulings are no longer an effective way to
maximize either equity or efficiency.
Document that court reliance on old hypotheses
about the impact of money, and their failure to
emphasize the benefits of structural reforms like
school size, increase inefficiency in educational
production functions.
Russell Harrison - Report on School Size and Education Outcomes - Page 126
AD HOC COMMENTARY ON PROPOSED RESEARCH PROJECTS:
It is respectfully suggested that to follow-up the present study, the New Jersey
Commission on Business Efficiency in the Public Schools should obtaining funding to
research the following issues.
Russell Harrison - Report on School Size and Education Outcomes - Page 127
10A: TEST SCORES
New research should examine how school size affects GEPA test scores as well as HSPT
scores. It is important to find out the extent to which school size hurts students in middle
schools as well as high schools.
New research should examine how school size affects residuals in test scores, to see
whether school size affects the efficiency of learning for different types of curriculum
and age levels. Section 4 outlines a methodology to guide this effort.
Russell Harrison - Report on School Size and Education Outcomes - Page 128
10B: CRIME AND VIOLENCE
10A1: The Commission should sponsor a follow-up study to examine individual schools
to document how size escalates problems of school crime and violence.
Prior research has measured school crime in New Jersey using districtwide
aggregates, to avoid embarrassing individual schools, and to minimize
measurement error. However, research should now proceed to look at crime in
individual schools. Does the relationship linking school violence with the size of
the student body, or perhaps the size of the school facility, or other indices of
school size sufficient to reject the null hypothesis looking at individual schools, or
a full sample of over 2,500 schools? How much does school size affect school
crime, controlling for DFG categories or other socio-economic variables? Which
kinds of schools are most efficient in controlling crime, relative to their levels of
spending, class size, poverty, minority race, special needs students, access to
computers, etc?
10A2: The Commission should sponsor a follow-up study to examine district size versus
school size.
Prior research on New Jersey suggests that district size has a major impact
on school administration. To what extent does school size affect student behavior
in a way that is separate and distinct from district size? More importantly, what
increases school problems like high school violence more ? big schools or big
districts?
Russell Harrison - Report on School Size and Education Outcomes - Page 129
TYPES OF CRIME
10C: The Commission should sponsor a follow-up study to examine violent versus nonviolent
school incidents.
Does school size produce multiplier effects on total school crime that are
similar to student violence? Do larger schools have disproportionate problems
with vandalism that increase the de facto costs of education, even when municipal
officials pay the costs of removal? How about other non-violent crimes?
The Commission should sponsor a follow-up study to examine and analyze nationwide
surveys to show that school size may be especially linked to violent versus non-violent
school crimes.
This research shows linkages of school size with the geographical
concentration of violence within certain types of high school districts.
Now research is needed to look both at New Jersey and in other states to
see how school size affects not only violence, but other indices of school crime.
In particular, to what extent does school size at specific tipping points exacerbate
the growth in violence versus non-violent school incidents? To what extent does
school size exacerbate school violence far more than less violent crimes like drug
and alcohol abuse among students, vandalism, or even carrying weapons?
10D: The Commission should sponsor a follow-up study to examine the impacts of drug
use that affects individual students versus school size that affects students collectively.
Prior research suggests that drug use is a major source of school crime and
violence. However, such may not be the case in New Jersey, at least compared to
the governance structures for schools. In New Jersey, which affects crime rates
more ? drug use, or school size? Does school size affect crime rates
independently of drug use? Do small school learning communities produce a
climate that overcomes the potential to student crime produced by problems of
drug use in the school community? Do large schools exacerbate relationships
between drug use and crime?
Russell Harrison - Report on School Size and Education Outcomes - Page 130
WHERE DOES SCHOOL SIZE HURT WORST?
10E: The Commission should sponsor a follow-up study to examine grade levels where
big schools hurt students worst.
Prior research suggests that the size of districts, classes, and schools may
produce bigger impacts on students at lower grades than at upper grades, like high
school. For New Jersey, is the evidence for lower grade level students similar to
the evidence for high school students? Is it possible that the effects of size may
actually be greater for students at lower grades? Alternatively, are the adverse
effects of school size exaggerated at upper grades?
In short, test prior research that suggests school size may hurt more at lower
grades than at upper grades
Walberg, H. J., and Walberg, H. J., III. "Losing Local Control." Educational
Researcher 23/5 (June/July 1994): 19-26. 1994
North Carolina State Board of Education, Department of Public Instruction,
Division of Accountability Services, Evaluation Section, School Size and Its
Relationship to Achievement and Behavior (Raleigh, North Carolina: NJ State
government, April 2000)
2000
10F: The Commission should sponsor a follow-up study to examine types of grade
configurations that exacerbate the adverse effects of school size.
What happens in schools or districts where the range of grades is
restricted, so students experience little continuity with the same teachers and
student peers? What types of grade configurations exaggerate the adverse effects
of school size?
o To what extent does the same harm due to school size found
among high schools in the state apply to elementary and middle
schools?
o Are the relationships significant enough for schools of all levels
that the null hypothesis can be rejected for all schools regarding:
? The relationship of school size with test scores (e.g., ESPA
and GEPA)
? The relationship of school size with both violence and less
violent forms of school crime found more often in lower
grade levels
? The relationship of school size with inefficiency at lower
grade levels.
Russell Harrison - Report on School Size and Education Outcomes - Page 131
COMPARING SCHOOL SIZE TO CLASS SIZE AND EXPENDITURES
10G: The Commission should sponsor a follow-up study to examine multiplier effects
from class size versus school size.
Certain prior research argues that class size is the major determinant of
academic outcomes. In contrast, Erik Hanushek, Ludger Woessman, and other
institutionalists have carefully reviewed the importance of class size nationwide.
Nationwide, smaller classes are not efficient means to improve education
outcomes, especially with respect to academic achievement.
What is the more appropriate conclusion for New Jersey? Is school size
more important than class size. If so, for what outcomes, at what levels of
education, and for what types of students?
?To what extent is there a decline in the importance of class size as a
determinant of educational outcomes, either over time, or as a given
cohort of students moves through grads 1-12. To what extent is the
importance of class size relative to school size minimized at higher levels
of education, when children are no longer confined to a single class
through the entire school day? What is the effect of school size on value
added by schools over time?
?Looking at all schools statewide, does school size exceed class size in
lagged multiplier effects on adverse educational outcomes, looking at
district test scores at all levels?
o Looking at all schools statewide, does school size exceed class size
in lagged multiplier effects on adverse educational outcomes, looking
at violence and other types of school crime at all levels?
o Looking at all schools statewide, does school size exceed class size
in lagged multiplier effects on adverse educational outcomes, looking
at dropouts and absenteeism at all levels?
o Looking at all schools statewide, does school size exceed class size
in lagged multiplier effects on adverse educational outcomes, looking
at inefficiency at all levels?
10H: The Commission should sponsor a follow-up study to examine and measuring
tradeoffs between changes in school size and class size.
To what extent would a balanced policy of trading off smaller schools for
larger classes a means to maximize efficiency in the delivery of public education.
Research is needed that would conduct an empirically-based computer simulation
to answer the following question:
o If a state like New Jersey should trade-off cuts in school size of 10
percent, with increases in class size of 10 percent, over a decade how
many hundreds of millions of dollars in revenues would be saved, how
much of a reduction in dropouts and absenteeism could be expected,
and how much of an improvement in test scores could be expected?
10I: The Commission should sponsor a follow-up study to examine the continuing
validity of the old thesis that Spending is a Panacea, versus the problems produced by
school size.
Prior court litigation implies that money is the major determinant of academic
outcomes in schools, especially during the 1970s and 1980s? However, is the underlying
premise of the ?public school finance reform litigation crusade? still valid?
Erik Hanushek has carefully reviewed prior research on the importance of
expenditures and other fiscal resources on educational outcomes nationwide.
Russell Harrison - Report on School Size and Education Outcomes - Page 132
Nationwide, spending and fiscal resources are not significant means to improve
educational outcomes, especially with respect to academic achievement. How valid is
this conclusion for New Jersey? In particular, is school size more important?
?To what extent is there a decline in how important money is as a
determinant of educational outcomes, either over time, or as a given
student cohort moves from grades 1 through 12? To what extent is there
declining importance in how much is spent, versus how and where it is
spent?
o To what extent is the importance of spending per student relative
to school size minimized at higher levels of education, when parental
resources are no longer as important as a determinant of spending
and/or successful educational outcomes
o Looking at all schools statewide, is spending per pupil as important
as school size in shaping educational outcomes over time?
o To what extent do the poorest [top-decile poverty] districts in New
Jersey now receive and spend more revenues than the richest [bottom
decile poverty] districts?
o Looking at all schools statewide, does school size exceed per
student spending in lagged multiplier effects on adverse educational
outcomes, looking at district test scores at all levels?
o Looking at all schools statewide, does school size exceed per
student spending in lagged multiplier effects on adverse educational
outcomes, looking at violence and other types of crime at all levels?
o Looking at all schools statewide, does school size exceed per
student spending in lagged multiplier effects on adverse educational
outcomes, looking at dropouts and absenteeism at all levels?
o Looking at all schools statewide, does school size exceed per
student spending in lagged multiplier effects on adverse educational
outcomes, looking at inefficiency at all levels?
o In the last 20 years, does a quantitative content analysis of state
court intervention into school finance cases been characterized by bias
in the degree to which courts focus on equity issues versus efficiency
issues, either in New Jersey or other state courts which provide
precedents for New Jersey courts? Has prior court intervention
resulted in a growth in costs over time for state a taxpayer that has
exceeded the growth in favorable educational outcomes, as outlined in
Goals 2000?
Russell Harrison - Report on School Size and Education Outcomes - Page 133
ANOTHER LOOK AT WHERE SCHOOL SIZE HURTS WORST
10J: The Commission should sponsor a follow-up study to examine what is the Optimal
School Size, or what are the critical tipping points for school size?
Prior studies have spent a lot of time debating the optimal size of schools.
Rarely have they used outcomes data to determine when big becomes too big.
Instead they generally focus on spending. However, when one also takes into
account variables like test scores, absenteeism, or dropouts, when does big
become too big? What are the key tipping points for size-outcome relationships?
o At what specific level of enrollment are the adverse effects of school
size especially prominent? Where is the break-even point between per
student spending and adverse educational outcomes like dropouts and
absenteeism? To what extent are the enrollment caps proposed in
other states, valid for New Jersey? What size tipping points are most
significant for elementary, middle, and high schools respectively?
o How do New Jersey tipping points for schools correspond to the
tipping points or caps proposed in prior research by:
? Oxley
? Lee and Smith
? The National Association of Secondary School Principals
? Howley and Bickel
10K: The Commission should sponsor a follow-up study to examine the extent to which
school size hurts equality goals.
Previous court decisions have spent a lot of time saying that school policy
should aim to achieve equality. However, generally the courts focused on
equality of inputs like money, and ignored equality of outputs like learning or
student behavior.
To what extent does school size affect equality of learning or student
behavior?
In New Jersey, to what extent does school size hurt more in poverty districts
and minority districts, or poverty schools and minority schools?
o To what extent is school size associated with the growth of inequality
among students in rich and poor districts? Where are academic effects
most adverse against at-risk students? To what degree does school
size maximize inequality of achievement, and deny students equal
access to a through and efficient education that benefits all children
equally, including students in poor and minority districts? To what
extent does school size exaggerate the adverse effects of poverty? To
what extent does school size exaggerate the adverse effects of minority
concentrations? To what extent does school size exaggerate the
combined effects of poverty and minority concentrations? To what
extent do poverty and minority concentrations exaggerate the adverse
effects of school size?
o How do the patterns for New Jersey correspond to the patterns found
in states like:
? Georgia
? Ohio
? Texas
? California
Russell Harrison - Report on School Size and Education Outcomes - Page 134
EVIDENCE OF ANOMIE AND ALIENATION
10L: The Commission should sponsor a follow-up study to examine and analyze
nationwide surveys to link school size, Parental Alienation, and lack of Involvement by
Parents in the life of the school.
Prior research suggests that school size is correlated with absenteeism by
students. How about absenteeism by parents? Is there nationwide evidence to
link school size with declining parental involvement in schools?
o To what extent does school size reduce the percent of parents who
actively and positively participate in the life of the school, and thus
increase the percent of teachers who report serious problems of
parental alienation, absenteeism, and apathy regarding their school?
10M: The Commission should sponsor a follow-up study to examine and analyze
nationwide surveys that link school size with the loss of consensus and rapport between
teachers and principals.
Prior research indicates that the most successful schools have a school
climate based on mutual ?trust? and a sense of ?connectedness? among staff.
Such elements are essential to successful ?restructuring?.
Is there nationwide evidence to link school size with alienation and animosity
among staff, or at least a loss of consensus?
?How much evidence is there to link school size with staff conflict and
disagreements, including a lack of consensus between teachers and
principals?
o To what extent does school size result in a lack of consensus
between teachers and principals on major problems facing the school,
and how to deal with them?
10N: The Commission should sponsor a follow-up study to examine and analyze
nationwide surveys that link school size with Physical Conflicts and Fear as problems
facing schools.
Prior research indicates that a pervasive sense of fear and intimidation is a
major problem in many school systems nationwide. Nationwide, school size may
be closely linked to physical conflicts, which shape psychological stress and
discomfort.
?How much nationwide evidence is there to link school size with fear and
intimidation among teachers and students?
o To what extent is school size correlated with a higher percent of
teachers reporting problems of fear and intimidation and physical
conflict that adversely affect the educational process?
o Does school size increase problems with physical conflicts and
fear among teachers independently of such status offenses as carrying
or owning weapons?
o Does school size increase problems with physical conflicts and
fear among teachers independently of zero-tolerance policies?
Russell Harrison - Report on School Size and Education Outcomes - Page 135
INDIRECT COSTS
10O: The Commission should sponsor a follow-up study to examine and analyze
nationwide surveys to link school size with the costs of construction, maintenance, and
transportation.
In prior decades traditional estimation processes for construction costs
indicated that schools with larger floor areas had lower costs per square foot. The
implication was that construction costs were lower for schools projected to have
larger enrollments. Such estimates ignored site acquisition costs. They also
ignored indirect costs for future maintenance and transportation.
What is the evidence today? Is there nationwide evidence to document
that school size has now become correlated with higher initial capital costs? Is
school size now correlated with inflated costs for maintenance and transportation,
whatever may have been the relationship in the distant past?
How about in New Jersey? Is there evidence for New Jersey that the
physical size of schools is associated with extra costs for maintenance and
transportation?
o To what extent does school size increase capital costs for schools,
based on a meta-analysis of recent surveys of capital construction costs
for school projects nationwide?
o To what extent does school size exaggerate the costs of dealing
with vandalism problems?
o To what extent does the physical size of individual New Jersey
schools affect the fiscal costs of dealing with academic problems,
dropouts, absenteeism? What is the square foot ?footprint? of each
school, and how does physical size compound inefficiency problems
with growing violence and declining test scores?
o To what degree is the physical size of schools correlated with
transportation costs?
10P: SUBURBAN SPRAWL
To what degree do larger schools cause distortions in land use patterns, encourage
suburban ?sprawl?, and discourage recycling and historical preservation goals in
cities? To what degree is school size associated with metropolitan ?sprawl?
indicators?
10Q: The Commission should sponsor a follow-up study to examine and analyze
linkages of school size with the need for school police and metal detectors.
Nationwide larger schools are far more apt to respond to problem of violence
with programs to place police in the schools, and metal detectors at the front
doors. The question is, do these responses help very much, compared to
preventive measures like the small school learning community?.
?Is there evidence to document that school size is correlated with the use of
remediation programs as Symbolic Responses to underlying problems,
even where such programs do not eliminate the underlying problems?
o To what extent does school size increase the need for remedial
programs and intervention strategies to deal with school violence and
other problems that increase costs for police and local taxpayers, and
divert resources from mainstream educational programs?
10R: The Commission should sponsor a follow-up study to examine the effect of large
schools on municipal tax rates, and aggregate local tax burdens.
Russell Harrison - Report on School Size and Education Outcomes - Page 136
Nationwide big schools are often found in urban communities faced with
major ?fiscal overloads?. For example, municipalities with big schools tend to
spend more on welfare and crime relative to taxable resources. How systematic is
the relationship of school size with municipal overload, and why?
?Is there evidence to document that school size is correlated with aggregate
municipal tax burdens among New Jersey communities?
o To what extent do communities with larger schools faced inflated
overall tax rates due to municipal overburdens from school crime, poor
achievement, subsequent unemployment and other problems among
dropouts and academic failures? To what extent are overall tax rates
higher in municipalities where districts build larger schools?
10S: The Commission should sponsor a follow-up study to examine the adverse effects of
school size on ?hedonic? house prices.
A previous study in Ohio indicates that where districts consolidate and big
schools produce big problems, the value of owner-occupied houses takes a nosedive
over time. What about New Jersey?
?Is there evidence to document that school size is correlated with
decreasing house prices [relative to expected market values given the
hedonic characteristics of the housing supply and the community].
o To what extent is school size negatively correlated with house
values? To what extent do districts with larger schools face declining
house values, similar to problems other states face where house values
decline over time in the face of inferior school quality like that found
in larger schools?
10T: The Commission should sponsor a follow-up study to examine and calculate the
extent to which dropouts deflate nominal spending costs for students in school, but
maximize actual fiscal costs for governments in general.
This research indicates that school size is linked to more dropouts. However,
once a student drops out, school costs may go down. Thus the linkage of school
size with actual costs is often unclear, either short term or long term?
?What is the full scope of the long-term fiscal costs that governments face
from dropouts?
o What are the total fiscal costs faced by federal, state, and local
government agencies from functional dropouts of the type
disproportionately produced by large schools?
?Large schools often seem to spend less than very small schools per
student. However, this often ignores the fact that large schools force large
numbers of marginal students to drop out. If one took into account
students who should be in school, but have dropped out, then the costs per
potential graduate would appear much higher in large schools.
o To what extent do districts with large schools actually cost more
per graduate, after subtracting out from nominal enrollments both de
facto and de jure dropouts who leave the school over time, including
students who flee the system after their families rent or buy new
houses in other districts to escape the problems produced by the
factory-model school.
10U: The Commission should sponsor a follow-up study to examine and document the
segregation effects of school size.
Russell Harrison - Report on School Size and Education Outcomes - Page 137
Large schools are often praised as an instrument to achieve integration. Are
they?
?Large schools in many states disproportionately force out middle class
families and their children from a district, leaving behind poverty students.
To what extent is school size correlated with metropolitan sprawl and
segregation of the poor in states like New Jersey?
o To what extent do large schools in center city districts constitute
?push? factors that isolate and concentrate poor students among the
students who remain, while becoming a major factor that encourages
metropolitan ?sprawl?.
o To what extent do patterns of sprawl and de facto segregation over
time for New Jersey resemble those for other educational systems in
areas like
? California
? New York
? Ohio
? England
10V: The Commission should sponsor a follow-up study to examine the effects of school
size on de jure versus de facto dropouts.
Jay Greene and others argue that many states obscure dropout rates by
only counting ?legally defined? dropouts. They fail to take into account how
many students fail to graduate on time with a regular diploma, versus potential
graduates predicted from prior enrollments by 7th, 8th or 9th grade students. Even
though students flee the schools, simply disappear into the underground economy,
or end up in jail, they are not counted as dropouts.
Is this a problem for many districts or schools in New Jersey? More
importantly, how does school size increase the need to look at de facto dropouts
versus de jure ?legally defined? dropouts? Using the Jay Greene index for de
facto dropout rates, how much does school size affect de facto dropouts, and how
much harm do these dropouts produce for themselves or for others?
Russell Harrison - Report on School Size and Education Outcomes - Page 138
A META-ANALYSIS OF INDIVIDUAL ATTITUDES AND BEHAVIOR
RELATIVE TO PUBLIC HEALTH RISK BEHAVIORS
10W: The Commission should sponsor a follow-up study to conduct a meta-analysis of
nationwide research to explain the effects of school size on Teacher satisfaction or
dissatisfaction with the school climate. The research should begin with evidence from:
Hard, S. ?Professional Learning Communities: What Are They and Why Are They Are
Important,? Issues About Change, Vol. 6, No. 1. Southwest Educational Development
Laboratory, 1997
1997
Fine, M. and Somerville, J. (eds.) Small Schools, Big Imaginations: A Creative Look at
Urban Public Schools. Chicago: Cross-City Campaign for Urban School Reform.
Eberts, R. W.; Kehoe, E.; and Stone, J. A. The Effect of School Size on Student
Outcomes. Final Report. Eugene, OR: Center for Educational Policy and Management,
University of Oregon, June 1982 (ED 245 382).
1982
10X: The Commission should sponsor a follow-up study to conduct a meta-analysis of
nationwide research to explain the effects of school size on Student satisfaction with the
school climate. . The research should begin with evidence from:
Edington, E. D., and Gardener, C. E. "The Relationship of School Size to Scores in the
Affective Domain from the Montana Testing Service Examination." Education 105/1 (Fall
1984): 40-45.
1984
Aptekar, L. "Mexican-American High School Students' Perception of School."
Adolescence 18/70 (Summer 1983): 345-357. 1983
Lindsay, P. "The Effect of High School Size on Student Participation, Satisfaction, and
Attendance." Educational Evaluation and Policy Analysis 4/1 (Spring 1982): 57-65. 1982
Russell Harrison - Report on School Size and Education Outcomes - Page 139
10Y: The Commission should sponsor a follow-up study to conduct a meta-analysis of
nationwide research to explain the effects of school size on Student involvement in
constructive extra-curricular activities, versus self-destructive drug use, alcohol abuse,
sexual promiscuity, crime, and violence. The research should begin with evidence from:
Holland, A., and Andre, T. "The Relationship of Self-Esteem to Selected Personal and
Environmental Resources of Adolescents." Adolescence 29/114 (Summer 1994): 345-
360.
1994
Stevens, N. G., and Peltier, G. L. "A Review of Research on Small-School Student
Participation in Extracurricular Activities." Journal of Research in Rural Education 10/2
(Fall 1994): 116-120.
1994
Schoggen, P., and Schoggen, M. "Student Voluntary Participation and High School Size."
Journal of Educational Research 81/5 (May/June 1988): 288-293. 1988
Green, G., and Stevens, W. "What Research Says about Small Schools." The Rural
Educator 10/1 (Fall 1988): 9-14. 1988
Hamilton, S. F. "Synthesis of Research on the Social Side of Schooling." Educational
Leadership 40/5 (February 1983): 65-72. 1983
Grabe, M. "School Size and the Importance of School Activities." Adolescence 16/61
(Spring 1981): 21-31. 1981
Huling, L. "How School Size Affects Student Participation, Alienation." NASSP Bulletin
64/438 (October 1980): 13-18. 1980
Barker, R., and Gump, P. Big School, Small School: High School Size and Student
Behavior. Stanford, CA: Stanford University Press, 1964. 1964