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Why Production Function Analysis is Irrelevant in Policy Deliberations Concerning Educational Funding Equity

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Hanushek and Walberg use production function methodology to contend that there is no relationship between school expenditures and student achievement. Production function methodology uses correlational methods to demonstrate relationships between input and output in an economic system. These correlational methods may serve to hide rather than reveal these relationships. In this paper threats to the validity of these correlational methods for analysis of expenditure-achievement data are discussed and an alternative method of investigation is proposed. The proposed method is illustrated using data from two states (Ohio and Missouri). The method demonstrates relationships between expenditures and achievement that were overlooked by the production function method.
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Education Policy Analysis Archives
Volume 1 Number 11 November 2, 1993 ISSN 1068-2341
A peer-reviewed scholarly electronic journal.
Editor: Gene V Glass, Glass@ASU.EDU. College of Education,
Arizona State University,Tempe AZ 85287-2411
Copyright 1993, the EDUCATION POLICY ANALYSIS
ARCHIVES.Permission is hereby granted to copy any article
provided that EDUCATION POLICY ANALYSIS ARCHIVES is
credited and copies are not sold.
Why Production Function Analysis is Irrelevant in Policy Deliberations
Concerning Educational Funding Equity
Jim C. Fortune
College of Education
Virginia Tech University
FORTUNE@VTVM1.BITNET
Abstract: Hanushek and Walberg use production function methodology to contend that there is
no relationship between school expenditures and student achievement. Production function
methodology uses correlational methods to demonstrate relationships between input and output
in an economic system. These correlational methods may serve to hide rather than reveal these
relationships. In this paper threats to the validity of these correlational methods for analysis of
expenditure-achievement data are discussed and an alternative method of investigation is
proposed. The proposed method is illustrated using data from two states (Ohio and Missouri).
The method demonstrates relationships between expenditures and achievement that were
overlooked by the production function method.
Introduction
"On 26 February 1988 Bennett remarked, `Money doesn't cure school problems.' On 29 February
1988 he was more explicit: `We've done 147 studies at the Department of Education. We cannot
show a strong, positive correlation between spending more and getting a better result.' In an
earlier reference to those studies, he had said on 13 April 1987 that `in only two or three do we
find even a weak correlation between spending and achievement.'" (Baker, 1991) The 147 studies
referred to by Bennett are those summarized by Hanushek (1986) using the production function
technique.
Hanushek (1989) contended that "Variations in school expenditures are not systematically related
to variations in student performance" and that "... schools are operated in an economically
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inefficient manner ." He suggested that "increased school expenditures by themselves offer no
overall promise for improving education" and that "school decision making must move away
from the traditional "input directed" policies to ones providing performance incentives." To
support his contentions, Dr. Hanushek relied on the 26 year old, much maligned study by
Coleman et al, Equality of Educational Opportunity, and his summary of 187 studies using
educational production functions.
Walberg appears to base his case contending no relationship between achievement and
productivity on his theory of causal influences on student learning and the resulting nine
productivity factors (1982), on the triad relationship of socio- economic status, productivity, and
expenditures (1989), and on Hanushek's model and the early literature related to production
function analysis (1984).
POLICY RELEVANCE OF THE PRODUCTION FUNCTION METHODOLOGY
Monk (1992) described production function analysis as the relating of an input measure to an
output measure using correlation or multivariate analysis (regression analysis). He reported that
production research began in education some 30 years ago. The process involves the study of
relationships between purchased schooling inputs and educational outcomes. The research,
according to Monk, is deductively driven, although the deductive arguments tend to be
abbreviated. He suggested that the approach has limited utility in policy research because of
methodological and conceptual limitations. Monk pointed out that recent research includes more
complex multivariate models which have greater potential for illuminating policy.
Both traditional production function analyses and the modern multivariate version to which
Monk alluded are based on correlational methods which are inadequate to deal with causation. In
the simple linear correlation model, a single input variable (often, expenditures, but sometimes
other school related inputs such as teacher experience or teacher preparation) is correlated with a
single output variable (usually achievement, but sometimes percent passing minimum
competency tests or rate of graduation). The multiple dimensionality of schooling suggests that
such simple representations of either input or output are inadequate to describe the production
relationships.
The second major production function analysis model is based on regression procedures, where a
single output variable is predicted by one or more input variables (chosen from expenditure data,
teacher experience or teacher preparation) and by intervening variables (such as socio-economic
variables, school size, and the like). The purpose of using the intervening variables is to control
factors which may confound the actual input-output relationship. In some applications the
researcher permits the intervening variables to enter the regression prior to the entry of the input
variables. There exists a serious problem with shared variance among the three sets of variables
that will be discussed later. Regression based on the prediction of the output variable residual
(which has been created by regressing the partial correlation residual of the intervening variables
controlling for their relationship to the input variables with the output variable) by the input
variables is a more appropriate application to control for confounding variables.
Problems with the Simple Linear Correlation Approach
The Assumptions of the Linear Correlation Approach. Application of the simple correlation
model must meet the data assumptions required by correlation, the limitations to inference
assumed in the use of the model, and the implicit assumptions about the relationship between
correlates inherit in the production function methodology. For the application of the Pearson's
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Product Moment Correlation it is required that one have near or better than interval data for
paired cases and that the full range of each variable be present. The coefficient attained measures
the linear relationship between the two variables and indicates association, but not necessarily
causation.
What Constitutes Differences in Expenditures? "Throwing a bucket of water on a raging fire will
not keep a building from burning to the ground, but no one would argue on the basis of this
experience that water has no value in fire-fighting. The value of water is apparent only when
enough is applied to overcome the fire by reducing the heat below a critical point, degrading the
fuel, or temporarily removing the air needed for combustion. An analogous situation often occurs
in education. Frequently, we judge an intervention strategy to be ineffective before we have
really implemented a program that is intense enough to achieve the desired effects.
"Compensatory education" is a case in point." (Bridge, Judd, and Moock, 1979)
The above phenomenon has been labeled a threshold effect. One reason why the correlation
method of production function analysis does not show effects of small differences of funding on
achievement is the threshold effect. One dollar difference in funding will not purchase a
commensurate or observable difference in achievement. Instead some larger, aggregate
differences in funding, perhaps $600 or $700, is needed to purchase observable differences in
achievement.
Perhaps the greatest problem in the use of the simple, linear correlation method beyond variable
specification, is the absence of the cost disparities that are essential to demonstrate differences in
educational purchasing power. An ordering of districts by amount of instructional expenditures
does not necessarily order the same districts by their educational purchasing power. One district
may have five dollars less in per pupil expenditure than a second district, but may have to pay on
the average ten dollars more per teacher than does the second district. Ordering of districts by
dollar differences which are less that the measurement error associated with expenditures results
in gross underestimation of the true relationship between costs and achievement.
The Truncated Variable (Attenuation). Percent passing a test as a measure of achievement
represents a somewhat unusual truncation of a variable in that the variance on the achievement
measure is limited to variation of dichotomies rather that variation across the full set of test
scores. Variable truncation also occurs when the tests have either floor or ceiling effects, when
only one specific segment of the enrollment is used (such as at risk students or college students)
or when data are not available for the entire sample being analyzed.
Potential Non-Linear Relationships. The simple, linear correlation method will not identify
non-linear relationships between the input and output variables. In one of the two states
discussed later in this paper, I found a quadratic relationship in exploring the data. A state
department report in the second state also alluded to a potential quadratic relationship between
input-output variables.
Problems with the Multiple Regression Approach
The Assumptions of the Multiple Regression Approach. The application of the regression
approach is characterized by a single output variable (some form of achievement measurement or
percent reaching an educational standard) being predicted by one or more input variables
(expenditures, teacher characteristics, and the like) and controlling for one or more background
variables (such as socio-economic variables or school size). Two ways are used to control for the
background variables. The first way is to permit the background variables to enter first in the
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prediction equation. The second is a residualizing technique. The residualization process
involves creating the residual of the output variable by regressing the first partial of the
controlling variables with the vector of predictors on the output variable. The linear combination
of the predictor variables are then regressed on the output residual. The regression approach
requires that the researcher meet all of the assumptions that have to be met in the simple, linear
correlation analysis. In addition, the researcher is required to have a theory or rationale for
establishing the order of variable entry and an understanding of the shared variance problem.
The Order of Variable Entry Problem. The order of variable entry in the calculation of the
correlation is important in handling shared variance or commonality of explanation. If two
correlated independent variables (predictors) are related to a dependent variable (outcome or
criterion), the first variable to enter into the regression calculation gets credit for all of its
correlation with the dependent variable. When the second variable is entered into the regression
calculation, it gets credit only for the correlation that it has with the dependent variable that has
not been explained by the first variable entered. Hence, the first variable gets credit for the
correlation with the dependent variable that is shared by the second variable. Critics of Coleman
showed that his order of effects do not hold up across applications of different regression models.
(Pedhazur, 1982)
The Shared Variance Problem. In dealing with this triad relationship created by the output
variable, the input variables and the controlling variables, Walberg (1989) simply failed to
discuss how he handled the shared variance problem inherit in the triad. His regression model
enters socio-economic status as the first predictor of students' test performances, size as the
second prediction variable, and finally expenditures as the third predictor variable. The amount
of explanation shared by socio- economic status and size and the amount of explanation shared
by socio-economic status and expenditures are credited to socio- economic status solely; the
amount of explanation shared by size and expenditures are then attributed to size alone. Certainly
not much variance remains to be explained by expenditures. A different order of entry would
produce markedly different results. Pedhazur (1982) credits Mayeske with the development of
commonality analysis to address this problem, but this methodology has been subjected to some
criticism. There is in fact no effective statistical method that will unconfound shared predictive
relationships. The only appropriate treatment of the shared relationship problem is, perhaps, a
straight-forward admission that it is the cause of the unresolvable ambiguity.
Other Design Problems for Both Correlational Models
Inadequate Variable Specification. In addition to the difficulty created by trying to represent
multiple inputs and outputs by single variables, there is the additional difficulty of including
confounding data elements in the input and output variable measurement. Selected single
variables may provide inadequate description of key inputs or outputs, may be unlikely to have
the relationship assumed by the production function paradigm, and may not be accurately
measured.
Inclusion of Confounded Data Elements. Federal dollars are included in school expenditures as
unrestrained expenditures. Some federal dollars are likely ear-marked for efforts that do not
contribute to student performance on achievement tests and some federal funds are not involved
in instruction. The inclusion of federal funds is not nearly the potential problem of some districts
testing special education students and including their scores in the test results. Hence, when there
is random confounding of the performance measure or the selection of a weak input variable,
each serves to reduce the size of relationships. The choice of percent passing a basic competency
test is an unfortunate choice of measure for an output variable. Percent passing immediately sets
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up a ceiling effect for those passing the test. The use of a dichotomized scoring process reduces
the amount of variance to be explained and attenuates the observed relationship.
Inadequate Determination of the Input Variables. Variable specification problems occur three
ways in the determination of input variables. Problems occur when input measures are chosen
that are not related to instruction. Perhaps, the most frequent example of this problem occurs in
the use of teacher salary as an input measure. Teacher salary is based on seniority and is likely
not related to quality of instruction. The second way that problems occur in the selection of input
measures is the selection of an input which cannot be measured adequately across all districts.
An example of this can be seen where school district size varies enough that economy of scale
enters into the accuracy of the measure. Very small districts require more dollars per pupil to
provide educational services equivalent to those of larger districts. The third way that selection of
input variables can create problems is when in some districts the input variable has larger
investment in special students than do other districts. Such cases are generated when districts
have a large number of "At Risk" students or where a district invests highly in advanced
placement instruction.
Inadequate Determination of the Output Variables. Variable specification problems occur in at
least four ways in the determination of output variables. The first way is when the output variable
that was chosen was a minor emphasis of many schools. Such may be the case when school
districts focus more on emotional, attitudinal, behavioral, or vocational outcomes. The second
way that dependent variable specification problems can occur is when there are floor and ceiling
effects to the measures. If the achievement measure has a ceiling or a floor effect, then many of
the students making a perfect or a zero score have accomplishments that are not being measured.
The third way that variable specification problems can occur is when the output variables have
no logical linkage to either the selected input variables or to school quality. An example of this
problem is the "Efficiencies" notion used by Walberg (1989). "Efficiencies" are school expected
output developed by the use of prediction based on socio-economic status. The variable can be
argued to better represent an error of measurement of the socio- economic construct than an
actual measure of school output. The fourth way that variable specification problems can occur is
the selection of an output measure that does not pertain to the whole student body. An example
of this is the selection of freshman grade point averages for their first year of college. Differential
proportions of students across districts go to college, college curriculum differ in difficulty and
colleges differ in difficulty.
Crossing Economic Eras. Production function studies are often grouped for interpretation and for
the making of policy recommendations. The 38 publications from which Hanushek extracted his
review range from the late 1950s to the early 1980s. This means that several of the studies were
conducted in different economic eras. In the 1950s, there was a dearth of federal funding, but
there was a wave of post-war resources and the early beginning of inflation. The 1960s brought
the Elementary and Secondary Education Act, increased federal funding, escalation of inflation,
baby boom growth beginning to enter schools and the emergence of civil rights as major issues in
education. The 1970s brought a slowing of federal funding, abatement of inflation and more
focus on growing enrollment. The 1980s marked a reduction in federal funds, the beginning of a
recession, the start of program retrenchment and the end of growing enrollment. It is quite likely
that input-output relationships differ across these four decades.
Inconsistent Determination of What is to be Considered a Production Function Study. Several of
the studies included in Hanushek's (1989) reviews do not have one or more of the elements
required to be classified as production function analyses. One such study is a study that occurred
in a large school district where teacher experience and differential teacher salaries were used as
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input variables. (Murname, 1975) In another study, college freshman grade-point-averages were
used as the output variable. (Raymond, 1968) It seems necessary that every study called a
production function analysis must have at a minimum an input variable, an output variable, an
assumption of a logical linkage between the school, total group and unbiased estimates for both
variables across the units of comparison and the computation of a correlational analysis.
Inadequate Sampling Representation. Problems with sampling representation occur in two ways:
through lack of disclosure and through inadequate sample size. Sampling becomes very
important in making an inference to a given population. In most production function analyses, the
intent appears to be that the researcher wishes to generalize to all of the school districts in the
United States. Not a single study or collection of studies appears to meet sampling requirements
for this inference.
Criticism of the Work of Hanushek
As Spencer and Wiley (1981, p. 44) suggested "Hanushek offers a provocative interpretation of
the last two decades of research on educational productivity." Unfortunately, "Hanushek
misinterprets the data on which he bases his conclusion and draws inappropriate policy
implications from them." (Spencer and Wiley, 1981, p. 41) After reading a sampling of
Hanushek's articles, I concur with Hughes (1992) that one could quote from 20 years of
Hanushek and destroy his current argument with his own words. However, I choose here to look
at his current thesis and see if it stands on its own foundation or falls.
Hanushek contended that "There is no systematic relationship between school expenditures and
student performance" (Hanushek, 1991, p. 425) and that "... schools are economically
inefficient." (Hanushek, 1986, p. 1166) He suggests that "increased school expenditures by
themselves offer no overall promise for improving education" (Hanushek, 1986, p. 1167) and
that "school decision making must move away from the traditional `input directed' policies to
ones providing performance incentives." (Hanushek, 1989, p. 49) To support his contentions, Dr.
Hanushek relies on the 26 year old, greatly criticized study by Coleman et al, Equality of
Educational Opportunity, Washington, D. C., Government Printing Office, 1966; and his own
summary of 187 (147 of these studies are those referred to by Bennett) studies of educational
production functions. (Hanushek, 1989, p. 46)
The Coleman Study as Support
The Coleman Study did indeed highlight input-output relationships across a large number of
districts, using a regression model. Coleman et al concluded that family characteristics and peer
group characteristics were more instrumental in promoting student achievement than were school
system characteristics. Critics of the study suggested that this ordering of effects may be due to
the analytic model used. Because the nature of regression analysis requires theory to specify
models and order of variable entry into the computations, Coleman received considerable
criticism, some of which resulted in George Mayeske's contributions to a new analytic technique,
commonality analysis (Pedhazur, 1982).
The order of variable entry in the calculation of the correlation is important in handling shared
variance or commonality of explanation. If two independent variables (predictors) are related to a
dependent variable (outcome or criterion) and are related to each other, the first variable to enter
into the computation gets credit for the correlation to the dependent variable that it shares with
the second variable. Hence, if a family variable enters first in the computation of the correlation
being used in predicting reading performance and then a peer variable enters into the calculation,
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the regression results will show for the family variable its unique correlation with reading
performance plus the correlation to reading performance that it shares with the peer variable. For
the peer variable only its unique correlation to reading performance is shown. Critics of Coleman
show that his ranking of effects does not hold up across applications of different regression
models. A second criticism of using Coleman as a primary research foundation lies in the age of
the Coleman data. Any economist should be able to see that time has likely made relationships in
the Coleman data obsolete with regard to today's economy.
Hanushek's Summary of Production Functions
Hanushek's (1989) summary of 187 studies of educational production functions is a continuing
theme throughout his publications. This summary began in 1981 with 29 articles and 130 studies,
it was continued in 1986 with 33 articles and 147 studies, and it was completed in 1989 with 38
articles and 187 studies. The summary is the research foundation for Hanushek's assertion of no
relationship between school districts' expenditures and student performance on standardized
achievement tests.
There are several serious omissions and research flaws in the description and logic of Hanushek's
summary. These include the lack of disclosure of sample sizes in the studies that were reviewed,
inadequacy in size and representativeness of the 187 case studies, misinterpretation of the results
of the hypothesis testing, potential misinterpretation of the summary, failure to use selected
research that is not consistent with the ideas being promoted (Glass and Smith (1979), Spencer
and Wiley (1981), Burstein (1980), and inadequate specification of the key variables.
Lack of Information on Sample Sizes in the Studies that Were Reviewed. The studies that were
reviewed by Hanushek were qualified in some unspecified manner. It appears that the primary
criterion for qualification was publication. Hanushek stated that at least one study deals with a
district or districts in all regions of the United States, with different grade levels, and across
different performance measures. He provided two tables that are purported to describe the
sample. In Table 1 of his 1989 article, "The Impact of Differential Expenditures on School
Performance," Hanushek showed the number of studies dealing with single districts (60) and the
number dealing with multiple districts (127), but he failed to provide any information on the
number of districts involved in the multiple districts. In his Table 2, Hanushek showed that 90
studies deal with at least one grade level in the range of grades from 1 to 6 and that 97 studies
deal with at least one grade level in the range of grades from 7 to 12. No attempt is made to show
replication across grade levels, number of students involved at each grade level or for each
district. With so few cases, the reader must wonder where the holes are in the sample.
Inadequate Size and Lack of Representativeness of the 187 Case Studies. There are
approximately 15,000 public school districts in the United States. These districts are
characterized by a large variance in total enrollment. Samples that include a majority of the
students and provide a confidence band of 0.95 percent are usually selected randomly using a
stratified sampling frame that involves the selection of approximately 800 districts (See the
Condition of Education Annual Reports by the National Center for Educational Statistics). A
simple random sample without control for the number of students covered requires
approximately 400 districts for a 0.95 percent confidence level and for representation (Schaeffer,
Mendenhall and Ott, 1986). The sample used by Hanushek was not random and was likely
smaller than either required sample sizes. The size is less bothersome than the scant likelihood of
randomness. The 187 studies were likely to have been conducted in reaction to some problem or
inquiry. Hence, are the relationships found in these unusual districts representative of those that
exist in the other 15,000? No evidence is presented to allow the reader to judge the
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generalizability of the results.
Misinterpretation of the Results of the Hypothesis Testing. In hypothesis testing, the researcher
assumes the null hypothesis and seeks reason to reject it. Failure to find such evidence does not
permit one to accept the null hypothesis, but only permits one to fail to accept the alternative
hypothesis. Failure to gather evidence that will lead to the acceptance of the alternative
hypothesis and the subsequent rejection of the null hypothesis may be due to inadequate sample
size, measurement errors or inaccurate model specification.
Spencer and Wiley (1981) used the 109 studies which were analyzed in 1981 by Hanushek who
sought to argue for the conclusion of no relationship between teacher-pupil ratio and the
performance of students as an example that illustrates another of Hanushek's difficulties with the
interpretation of significance tests on regression coefficients. Their argument showed that the
null hypothesis can be rejected for positive results and then can be rejected for negative rejects;
pointing out difficulty with the model used and the data set.
Potential Misinterpretation of the Summary. Baker (1991) discussed Hanushek's absence of a
decision rule in his summary of the literature for the 147 studies (Hanushek, 1986). He stated that
a synthesis of literature as reported by Hanushek can be conducted in one of two ways: either by
the vote counting method with a stated expectancy or decision rule or by the meta- analysis
method. Hanushek did not compute effect sizes so his review must have entailed by the vote
counting method. Given the absence of the statement of a decision rule by Hanushek, Baker
assumed a decision rule that 5% of the studies will be significant by chance. He then showed that
20% of the studies are significant, thus ruling out a chance relationship (Baker, 1991).
In Table 3 of his 1989 article, "The Impact of Differential Expenditures on School Performance,"
Hanushek showed the expenditure parameters for the 187 studies for seven educational inputs as
they relate to student achievement test performance. Although he reported number of studies, he
did not report number of districts, number of students, or grade levels to which the studies
pertain. For the various components he reports the number of non-significant studies found.
Hence, 82% of the 152 studies relating teacher/pupil ratio to student performance were found not
significant (p<0.05); 88% of the 113 studies relating teacher education to student performance
were found not significant (p<0.05); 64% of the 140 studies relating teacher experience to
student performance were found not significant (p<0.05); 78% of the 69 studies relating teacher
salary to student performance were found not significant (p<0.05); 75% of the 65 studies relating
expenditures per pupil to student performance were found not significant (p<0.05); 87% of the
61 studies relating administrative inputs to student performance were found not significant
(p<0.05); and 84% of the 74 studies relating facilities to student performance were found not
significant (p<0.05). For four of these seven inputs (Teacher experience, Teacher salary,
Expenditures/pupil, and Administrative inputs) ratios of the significant to non- significant studies
are equal to or exceed 11 to 4 odds in favor of positive relationships.
Failure to Cite Research that is not Consistent with the Ideas Being Promoted and Inadequate
Specification of the Key Study Variables. Given Hanushek's liberal qualification of studies and
his reliance on the Coleman study, his rejection of the Glass study as being subject to too much
criticism for attempting to calculate effect sizes for different class size intervals is surprising and
unaccountable. Hanushek's failure to address the criticisms of Spencer and Wiley was also
surprising. In his discussion of aggregation effects, the work of Burstein was overlooked. This
work demonstrates the potential danger of aggregated data and correlation.
Inclusion of Confounded Data Elements. Federal dollars are included in school expenditures as
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unrestrained expenditures. Some federal dollars are ear-marked for efforts that do not contribute
to student performance scores. An even more serious potential problem is that some districts test
special education students and other districts fail to test special education students. Hence, there
is random confounding of the performance measure, reducing the sizes of correlations possible.
Choice of Performance Measure. The choice of percent passing the basic competency test (bct) is
an unfortunate choice of measure for a performance indicator. Percent passing immediately sets
up a ceiling effect for those passing the test. Even if they benefit from additional or redistributed
expenditures, their gains can never be shown in the scattergrams. Gains shown by those who pass
and by those who continue to fail are not reflected in the measure.
Baker (1991) noted that another major problem is Hanushek's failure to correct correlations for
attenuation arising from the fact that per pupil expenditures are truncated. Baker stated that the
correlation between achievement and expenditures is greatly reduced because "no schools spend
a great deal more or less than others. ... It is quite easy for a significant finding to be overlooked,
if the observed data come from the center of a scattergram, where the attenuated data often
appear to be random. (Baker, 1991, p. 4)
Criticism of the Work of Walberg
Walberg appears to base the case for no relationship between achievement and expenditures on
his theory of causal inferences on student learning and the nine productivity factors (1982); on
the triad relationship of socio-economic status, productivity, and expenditures (1989); and on
reliance on Hanushek's model and on the early literature related to production function analysis
(1984).
Theory of causal inferences on student learning and the nine productivity factors
Walberg's review of productivity research and his development of the "theory" of school learning
has received much professional praise. I am in agreement with this praise in that the model
appears to synthesize a large body of research clearly and usefully. Walberg's model includes a
paradigm connecting Aptitude (ability, development and motivation), Instruction (amount and
quality), and Environment (home, classroom, peers and television) as inputs to Learning
(affective, behavioral and cognitive). I believe that this model is an accurate picture of a subset of
variables that are precursors of productivity. My experience suggests that curriculum probably
should not be ignored and left out of the model. Also, note that no variable entitled "expenditure"
is included directly in the model. Yet, expenditures are represented indirectly in both Instruction
and Environment. Walberg recognized this role in the following statement, "... and expenditure
levels of schools and districts, and their political and sociological organization - are less alterable
in a democratic, pluralistic society; are less consistently and powerfully linked to learning; and
appear to operate mainly through the nine factors in the determination of achievement."
(Walberg, 1982, p. 120) What is puzzling about about this statement is that Walberg appears to
be trying to stretch logic to agree with Hanushek's weak and inconsistent position, and reasons
that higher expenditures follow quality instruction rather than higher expenditures serve as
mediating factors to the purchase of quality instruction.
The triadic relationship of socio-economic status, productivity, and expenditures
Walberg appears to be interested in the triadic relationship of socio-economic status, productivity
(or at least efficiency of student test performance), and expenditures. This interest is expressed in
several studies and reviews authored by Walberg. In several of the studies, Walberg appears to
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have problems in the specification of at least two or perhaps all three of the variables of the triad.
Perhaps, one of the major problems with how Walberg has set out to study these variables is his
lack of control of certain key school variables. In the discussion of studies of the relationship of
class size to achievement test performances nothing is said as to how many of the small classes
were made up of special education students or were composed for remediation. The overlooking
of these two common practices in school certainly confounds the study of class size and the
inclusion of special education students confounds the measure of student performance in reading,
mathematics, science or other standard school curricula criteria used to define school
productivity. In his studies of district size, he permits urbanism to confound his variable.
Walberg is frequently unclear as to what is being measured as a variable representing
productivity. Sometimes his productivity variable is measured as percent passing. The method of
measurement clearly restricts the range of the achievement construct and serves to reduce the
observed correlation. At other times, Walberg uses what he refers to as an efficiency measure,
which is made up of the predicted achievement score using socio-economic status in the
prediction equation divided by the observed achievement score. This configuration called
"efficiency" appears to more closely represent a measure of prediction error for socio-economic
status. Clearly, his expenditure data include funds for transportation, lunch, special education,
and similar programs which do not bear directly on instruction.
In dealing with this triadic relationship, Walberg simply fails to discuss how he has handled the
shared variance problem inherent in the relationship. His regression model enters socio-
economic status as the first predictor of students' test performances, size as the second prediction
variable, and finally expenditures as the third predictor variable. The amount of explanation
shared by socio-economic status and size and the amount of explanation shared by
socio-economic status and expenditures are credited to socio-economic status solely; the amount
of explanation shared by size and expenditures are then attributed to size alone. Certainly, not
much explanation remains to be credited to expenditures. A different order of entry would
produce markedly different results. Mayeske developed commonality analysis to address this
problem, but the methodology has been subjected to some criticism. In actuality there is no
effective statistical method that will unconfound shared predictive relationships. Appropriate
treatment of the shared relationship is perhaps a straight-forward discussion of the irresolvability
of the problem.
Reliance on Hanushek's model
Walberg depends in several literature reviews on the productivity analyses reported by
Hanushek. He appears to rely on them without critical scrutiny and uses Hanushek's work
as rationale for demoting the role of expenditures in his model and in further analyses.
Walberg's acceptance without question of Hanushek's work raises some concern about the
other studies that he uses in his argument.
Regression Analyses of New Jersey Data
The analyses performed for the New Jersey hearings (Walberg, 1989) appear to duplicate
many of the faults discussed in Walberg's triad studies, and potentially contain a few new
variances from standard research practice. On page 43 lines 4 and 5 of the 1989 document,
Walberg's description of regression analyses is misleading. Regression analyses does not
provide a method of simultaneous analysis of the predictive contribution of three variables.
Order of entry attributes shared variance of two variables to the first one entered into the
prediction process. Observed relations are most likely not independent; only the last
variable to enter in the equation is likely to be independent.
11 of 22
Variable specification is again a problem as confounding other school factors such as
special education, remediation processes, transportation costs, and the lunchroom
expenditures have not been removed from the studies. It appears that the variable
"expenditures" rather than "expenditures per student" was run in the correlations. The
"Efficiencies" prediction is still used as a dependent variable and the truncated
measurement of productivity (such as percent passing) is used in several of the achievement
measures.
Order of entry and the problem of shared variance is a problem in these analyses. One
wonders what kind of discussion would ensue if an appropriate expenditure variable was
entered first in the prediction of test performances that had not been truncated or obscured
by the use of ratios.
Demonstration of the lack of validity of the production function methodology
A Suggested Alternative Approach
The production function method must be altered in three ways to make it policy relevant.
To identify the effects of large versus small expenditures, the research task appears to
demand a comparison rather than an association. Rather than asking if there is a
consistent relationship across the whole population, it is better to ask for what kinds of
districts do such effects exist within a state. A third change is to create a discrepancy in
expenditures large enough to reveal differences in the purchasing power of educational
services.
Finding Homogeneous Sets of Districts. Districts within a state differ on many dimensions.
Furthermore, the dimensions that are most discriminating in one state may not be so in
another. By grouping districts in a particular state into classes (e.g., rich vs. poor)
according to the key dimension for that state (e.g., wealth), homogeneous subgroups can be
obtained for further analysis. Size of districts, rural/urban, and number of exceptional
children (either gifted or at risk) are variables whose subdivisions are likely to establish
subsets of homogeneous groups. In states like Montana and Missouri, size is the dimension
which creates homogeneous subgroups. In Alabama rural/urban is the variable that yields
homogeneous subgroups. In Ohio, income levels or socio-economic status creates
homogeneous subgroups. In some cases, there are one or two large, poor, urban districts
which have to be considered as outliers so as to establish homogeneous subgroups.
Creating the Disparity in Funding. In 1970 a study conducted for the Office of Panning and
Program Evaluation/Bureau of Elementary and Secondary Education/United States Office
of Education found that approximately 300 dollars was needed to improve elementary
school children's reading scores one month over the course of a year. A proration of this
finding suggests that a disparity of 600 to 700 dollars is needed between districts compared.
Within each homogeneous subgroup, the districts are ordered by instructional
expenditures and then divided into two groups where one is formed by the upper 30% and
the other is defined by the lower 30%. The two groups are equal with regard to sample size
and differences between the groups on expenditures should exceed 600 dollars. Given the
satisfaction of these conditions differences in achievement scores should be apparent, if
they exist.
Using t-Tests to Investigate the Results of the Disparity. Given the creation of the two groups
(upper and lower 30%) from a single homogeneous subgroup and the verification of a 600
12 of 22
dollars disparity, the independent t-test with pooled variance can be used to discover
achievement test differences. If more than three homogeneous subgroups are to be
analyzed, methods to deal with the inflation of the confidence level should be considered.
Such methods include the recalculation of the confidence levels compensating for the use of
several t-tests (the Bonferonni procedure) or the use of the family of t-tests notion (e.g., the
Tukey procedure).
The proposed model can be used to investigate either a family of dependent or independent
variables or both. The use of several t-tests provides the method for including a number of
dependent or output variables. The ordering of districts for the determination of the upper
30% and lower 30% with regard to the input or independent variables permits the
consideration of any number of independent variables.
Application of the Alternative Approach to Two States
Data for the states of Missouri and Ohio were obtained through Education Policy Research,
Incorporated which participated in the suits involving equity of the state system for funding
the public schools. These data involved the per pupil expenditure data, the proxy data for
socio-economic status of the attendance area of the districts, district enrollment, and
achievement data which were used in the preparation of the cases by both sides in the
lawsuit. The achievement data for Missouri are the Missouri Mastery Achievement Test
(MMAT) prepared by the state to measure state objectives for the year 1990-91. The
achievement data for Ohio are NCEs from standardized achievement tests selected by the
districts for the year 1989-90. Both sets of achievement data are judged to have adequate
reliability.
In Table 1 are shown the production function correlations for the achievement data for the
school districts in Missouri. Note that there is only one correlation, the one for tenth grade
mathematics, that is large enough to be judged statistically significantly different from
zero. Since there are twenty production functions, one would conclude from such an
analysis that the production function shows no relationship between instructional costs and
achievement in Missouri.
Table 1: Correlations Between Expenditures per Student and Student Performance on MMAT
Achievement Tests
GRADE SUBJECT AREA
Reading Mathematics Science Soc Studies
4th (n=509) 0.050 0.073 -0.008 -0.025
6th (n=522) -0.026 -0.044 -0.108 -0.062
8th (n=519) -0.024 -0.019 0.027 0.012
9th (n=392) -0.005 0.077 0.077 0.072
10th (n=433) 0.049 0.117* 0.027 0.065
* denotes p<0.05
In Table 2 are shown the t-tests resulting from a partial application of the alternative
approach which creates the funding threshold not included in the production function
13 of 22
analyses for the twenty distributions of achievement data. The creation of the threshold
results in two of the distributions showing significant positive relationships using the
Bonferonni procedure. Ten of the twenty t-tests reach significant levels for single
applications for the t-test. Given the family-wise results, it remains risky to conclude a
positive relationship between achievement and per pupil expenditures at this time.
Table 2: Contrasts of High and Low Funded Districts on the Missouri MMAT
for 1990-1991
Per Pupil Expenditure Averages: Upper 30% = $2056.79 Lower 30% = $1248.48
Subject Group Mean Std Dev n t Sign.
4th Grade
Reading
High
Low
316.32
309.36
25.64
24.07
154
154
2.441 ns
4th Grade
Math
High
Low
313.47
306.87
33.75
25.49
154
154
1.934 ns
4th Grade
Science
High
Low
330.33
329.48
41.01
32.05
154
154
0.367 ns
4th Grade
Soc.Studies
High
Low
336.18
334.14
36.79
34.04
154
154
0.529 ns
6th Grade
Reading
High
Low
309.83
307.47
27.54
23.56
158
158
0.737 ns
6th Grade
Math
High
Low
360.12
358.82
42.67
34.39
158
158
0.298 ns
6th Grade
Science
High
Low
340.02
353.27
41.81
38.28
158
158
-0.942 ns
6th Grade
Soc.Studies
High
Low
323.94
323.31
32.54
31.19
158
158
0.175 ns
8th Grade
Reading
High
Low
325.98
322.97
24.26
24.30
156
156
1.088 ns
8th Grade
Math
High
Low
341.92
336.19
40.07
36.16
156
156
1.318 ns
8th Grade
Science
High
Low
365.41
360.96
44.25
37.45
156
156
0.955 ns
8th Grade
Soc.Studies
High
Low
326.32
321.08
27.26
24.84
156
156
1.764 ns
9th Grade
Reading
High
Low
294.13
287.63
22.59
18.94
131
131
2.198 ns
14 of 22
9th Grade
Math
High
Low
312.61
299.64
35.81
23.17
131
131
2.961 0.05
9th Grade
Science
High
Low
367.99
357.41
37.51
31.98
131
131
2.143 ns
9th Grade
Soc.Studies
High
Low
316.89
309.49
24.85
20.34
131
131
2.295 ns
10th Grade
Reading
High
Low
311.82
306.89
24.52
18.36
144
144
1.693 ns
10th Grade
Math
High
Low
339.80
330.52
32.30
20.31
144
144
2.525 0.10
10th Grade
Science
High
Low
347.97
343.79
29.23
23.54
144
144
1.180 ns
10th Grade
Soc.Studies
High
Low
309.53
306.03
24.59
18.47
144
144
1.196 ns
Application of the full alternative model involves not only the creation of the threshold, but
also the elimination of outliers or of extreme scores which may have an unusual
relationship between instructional expenditures and achievement. Such scores come from
economies of scale effects in small districts, the concentrating of at-risk students, or the
amassing of more than essential wealth. In order to complete the comparison, production
function analyses were performed on the twenty distributions after the outliers had been
eliminated. In the Table 3 are reported the results of these production function analyses.
Significant non-zero correlations are found for four of the twenty coefficients: fourth grade
reading, eighth grade reading and social studies, and ninth grade mathematics. The
significant correlation for tenth grade mathematics was lost in the elimination of the
outliers. However, only three of the correlations in Table 3 are negative, while nine are
negative in Table 1. Still these four non-zero correlations make concluding a relationship
between instructional expenditures and achievement too risky. The outliers removed were
school districts with enrollments less than 300 and enrollments of greater than 25,000
students.
Table 3: Correlations Between Expenditures per Student and Student Performance on MMAT
Achievement Tests with Outliers Removed.
GRADE SUBJECT AREA
Reading Mathematics Science Soc Studies
4th (n=329) 0.142** 0.107 0.019 0.096
6th (n=329) 0.048 -0.026 -0.052 0.015
8th (n=329) 0.132* 0.066 0.078 0.121*
9th (n=268) 0.063 0.146** 0.055 0.080
10th (n=318) 0.023 0.052 -0.029 0.023
15 of 22
* denotes p<0.05
** denotes p<0.01
In Table 4 are reported the results of the full application of the alternative model. Note that
the threshold is about $620 dollars and that the number of districts has now been reduced
to 331. Eight of the twenty t-tests are significant for Bonferonni calculated alpha levels.
Fourteen of the twenty t-tests reach the level of significance for unadjusted t-test
probabilities. These results permits the conclusion of a positive relationship between
expenditures per student and achievement on the MMAT. Missouri school districts can be
characterized by a large number of districts with fewer than 300 student enrollment, a few
extremely large districts which have a majority of high risk students and high
expenditures, and a handful of rich districts that have extremely high expenditures.
Table 4: Contrasts of High and Low Funded Districts with Outliers Removed on
Missouri MMAT for 1990-1991
Per Pupil Expenditure Averages Upper 30% = $1906.43 Lower 30% = $1284.22
Subject Group Mean Std Dev n t Sign.
4th Grade
Reading
High
Low
321.17
310.44
23.21
19.20
99
99
3.451 0.01
4th Grade
Math
High
Low
317.13
307.06
24.14
21.26
99
99
3.012 0.05
4th Grade
Science
High
Low
336.67
332.89
28.91
27.15
99
99
0.914 ns
4th Grade
Soc.Studies
High
Low
345.71
334.78
27.57
26.05
99
99
2.764 0.05
6th Grade
Reading
High
Low
312.33
306.98
20.66
18.16
99
99
1.921 ns
6th Grade
Math
High
Low
363.47
358.70
34.60
30.54
99
99
1.020 ns
6th Grade
Science
High
Low
358.25
354.46
36.77
34.01
99
99
0.748 ns
6th Grade
Soc.Studies
High
Low
327.97
322.62
26.53
24.13
99
99
1.472 ns
8th Grade
Reading
High
Low
327.68
319.13
16.69
17.67
99
99
3.280 0.05
8th Grade
Math
High
Low
344.05
333.20
34.44
30.18
99
99
2.338 ns
16 of 22
8th Grade
Science
High
Low
371.37
359.66
34.25
32.64
99
99
2.544 0.10
8th Grade
Soc.Studies
High
Low
329.59
319.24
21.13
21.13
99
99
3.419 0.01
9th Grade
Reading
High
Low
293.30
288.01
17.25
18.21
81
81
2.848 0.05
9th Grade
Math
High
Low
311.95
300.58
26.83
23.32
81
81
2.808 0.05
9th Grade
Science
High
Low
366.42
357.01
28.53
29.60
81
81
2.014 ns
9th Grade
Soc.Studies
High
Low
316.33
309.24
19.74
19.15
81
81
2.275 ns
10th Grade
Reading
High
Low
311.73
308.55
17.13
17.09
93
93
1.263 ns
10th Grade
Math
High
Low
338.46
332.03
21.65
19.87
93
93
2.089 ns
10th Grade
Science
High
Low
347.79
345.40
19.55
23.34
93
93
0.755 ns
10th Grade
Soc.Studies
High
Low
308.67
306.85
17.31
18.53
93
93
0.689 ns
A similar sequence of analyses has been performed for data obtained for the state of Ohio.
Production function analyses were performed on the number of school districts in the state
and contrasted with the results of t-tests performed after a threshold had been created.
This sequence comparing production functions with t-test contrasts was then repeated after
outliers were removed.
In Table 5 are reported the nine production function analyses for Ohio. None of the nine
achievement areas shows significantly non-zero correlations. In Table 6 are reported the
t-test contrasts for the same nine Ohio distributions. None of the nine contrasts reach the
Bonferonni significance levels.
Table 5: Correlations Between Instructional Expenditures and Selected Variables in Ohio
Database
Selected Variables
District Instructional
Expenditures per Student
4th Grade Reading -0.012 n = 608
4th Grade Language Arts -0.065 n = 608
17 of 22
4th Grade Mathematics -0. 024 n = 608
6th Grade Reading 0.008 n = 608
6th Grade Language Arts -0.019 n = 608
6th Grade Mathematics -0.006 n = 608
8th Grade Reading 0.004 n = 608
8th Grade Language Arts -0.028 n = 608
8th Grade Mathematics -0.002 n = 608
Table 6: Contrasts (t-tests) of School District Expenditures on
Achievement Scores
Per Pupil Expenditure Averages
Upper 30% = $2442.62 Lower 30% = $1578.16
n = 183 ... n = 183
Achievement Area Group Mean
St
Dev
t Sign.
4th Reading
high
low
54.95
54.27
5.93
5.45
1.133 ns
6th Reading
high
low
54.27
53.34
5.74
5.90
1.514 ns
8th Reading
high
low
54.79
54.07
5. 41
5. 36
1. 264 ns
4th Language
high
low
53.82
53.18
6.79
6.29
0.041 ns
6th Language
high
low
53.05
52.36
6. 21
6. 30
1.057 ns
8th Language
high
low
53.73
53.30
6. 25
6. 23
0.648 ns
4th Math
high
low
52.73
51.88
7.50
7.41
1.081 ns
6th Math
high
low
53.46
52.15
7.03
7.29
1.740 ns
8th Math
high
low
53. 70
52. 43
7. 31
6.89
1.712 ns
In Tables 7 and 8 are reported the same analyses after the outliers have been removed from
18 of 22
the achievement distributions. In Table 7 are reported the production functions.
Table 7: Correlations Between Instructional Expenditures and Selected Achievement Variables
in Ohio Database with Outliers Removed 1989-1990.
Selected Variables
District Instructional
Expenditures per Student
4th Grade Reading 0.053 n = 458
4th Grade Language Arts 0.034 n = 458
4th Grade Math 0.071 n = 458
6th Grade Reading 0.055 n = 458
6th Grade Language Arts 0.037 n = 458
6th Grade Math 0. 074 n = 458
8th Grade Reading 0. 072 n = 458
8th Grade Language Arts 0. 024 n = 458
8th Grade Math 0.091* n = 458
* denotes p<0.05
The nine production functions reported in Table 7 include only one non-zero correlation,
for eighth grade mathematics. From these analyses one is led to conclude no relationship
between instructional expenditures and achievement in Ohio. In Table 8 five of the nine
t-test contrasts show positive relationships leading to the conclusion that instructional
expenditures are related to achievement, demonstrating the inefficiency and
inappropriateness of production function analyses.
Table 8: Contrasts (t-tests) of School District Expenditures on Achievement Scores with
Outliers Removed Ohio Database, 1989-90.
Per Pupil Expenditure Averages
Upper 30% = $2187.07 Lower 30% = $1544.76
n = 106 ... n = 106
Achievement Area Group Mean St Dev t Sign.
4th Reading
high
low
55.09
53.64
6.23
5.44
1.714 ns
6th Reading
high
low
54.42
52.59
5.91
5.80
2.253 0.10
8th Reading
high
low
55.26
53.25
5.24
5.52
2.703 0.05
19 of 22
4th Language
high
low
53.84
52.89
6.91
6.27
1.042 ns
6th Language
high
low
53.23
51.64
6.29
6.42
1.805 ns
8th Language
high
low
53.94
52.56
6.17
6.33
1.603 ns
4th Math
high
low
53. 44
51.08
7.85
7.21
2.258 0.10
6th Math
high
low
53.94
51.15
7.36
7.26
2.759 0.05
8th Math
high
low
54.00
51.49
7.60
7.18
2.454 0.10
Conclusion
Production function analyses have been used to assist policy deliberations concerning
educational funding equity. These analyses are based on correlational methods which can
be misleading in the investigation the relationship between student achievement and
instructional expenditures. The correlation process fails to create a threshold of dollars
needed to demonstrate differences in achievement. An alternate method has been developed
for the investigation of the relationship. This method is based on creating homogeneous
subgroups of districts which are then ordered by expenditures per student. The
achievement mean for the group created by the highest funded 30% of the districts is
compared to the mean for the group created by the lowest funded 30% of the districts
using a t-test. This method was used to demonstrate relationships missed by production
function analyses in two states.
References
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Bridge, G.R., C.M. Judd, and P.R. Moock, The determinants of educational outcomes: The
impact of families, peers, teachers, and schools, Cambridge, Mass., Ballinger Publishers,
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Burstein, Leigh, "Issues in the Aggregation of Data," in Berliner, David, (ed), Review of
research in education, Vol. 8, Washington, D. C., American Education Research
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Coleman et al, Equality of educational opportunity, Washington, D. C., Government
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Virginia, 1992.
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Productivity in Twelve Countries." British Educational Research Journal, 12(3), 1986, pp.
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Walberg, H. J., "Improving the Productivity of America's Schools." Educational
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Copyright 1993 by the Education Policy Analysis Archives
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22 of 22
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... Os de Bowles (1970) e Levín (1976) encontram-se entre os clássicos. Já Fortune (1993) realiza extenso e exaustivo resumo detalhado de cada um dos obstáculos e defeitos das regressões e dos modelos que contêm. o corolário resultava mais ou menos óbvio: ou não se deve continuar aumentando o salário, ou deve-se atrelá -lo a algum elemento de produtividade. ...
... Caso relacionássemos o baixo nível de gastos e salários docentes em nossos países, provavelmente encontraríamos, da mesma forma, esta ausência de relação, mas por motivos bem distintos: diante de níveis tão baixos, um amento nas remunerações ou nos gastos em geral não significaria necessariamente que não haveria influência na qualidade da educação (independente de como se deseje ou possa medi-la). A revista Fortune (1993) compara este fato a um incêndio que se tentasse apagar com um único balde de água: de forma alguma ficaria demonstrado – ou alguém se aventuraria a afirmar – que, diante desta situação, a água seja incapaz de apagar o fogo. A quantidade é, simplesmente, insuficiente. ...
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O presente estudo tem como objetivo identificar características comuns entre os professores que pediram exoneração nas redes municipais de educação de São Bernardo do Campo e Diadema, bem como compreender os motivos que os levaram a tomar tal decisão. A pesquisa foi realizada por meio de questionário semiestruturado e, no total, obteve 74 respondentes. Os resultados da pesquisa indicam similaridades entre a maioria dos respondentes das duas redes: são professoras, com idade entre 26 e 45 anos, que pediram exoneração do cargo de professor para exercerem outras atividades dentro da mesma rede de ensino ou para exercerem a docência em outras redes que apresentavam melhores condições de trabalho e remuneração.
... The existing research focuses on the investment of financial power in education and the distribution of educational resources. These aspects have achieved certain results but there are still several problems (Card & Krueger, 1996;Pritchett & Fulmer, 1997;Hanushek, 1997;Fortune, 1993;Hodas, 1993;Levin, 1993;Colbert, Reuven & Levary, 2000;Breu & Raba, 1994;Izadi, Johnes, Oskrochi & Crouchley, 2002): (1) The research basically takes compulsory education as the object, which is more comprehensive, but it also results in the lack of research on the measurement index system and method of compulsory education resource allocation balance; ...
Article
Based on the reality of the Chinese government's promotion of the integration of urban and rural compulsory education, this paper proposes the concept of the compulsory education resource allocation Gini coefficient and comprehensive balance of compulsory education resource allocation and defined that the balance of compulsory education resource allocation can be reflected through the comprehensive equilibrium of compulsory education resource allocation. This paper proposes a compulsory education resource allocation balance measurement index system of two parts, which are a mandatory indicator system and a control index system, with the former being the minimum standard that must be met. Based on the PSR theory, a control index system consisting of 3 dimensions and 12 indicators is constructed from three aspects: pressure, state, and corresponding dimensions. This paper proposes a method of measuring the Gini coefficient of compulsory education resource allocation and the allocation balance of compulsory education resources, and verifying the feasibility of theoretical research through cases.
... Research findings about the significance of this variable tend to be ambiguous. While some works find no systematic relationship between school expenditures and variations in learner scholastic achievement, others show weak or strong relationships (Hanushek, 1986;Fortune, 1993 Ambiguous results are also found with regard to other correlates of wealth, such as class size (USA DOE), technology (Cohan, 1994;Warschauer, 2000;Novak and Hoffman, 1998;), the quality of the faculty (Michelson, 1970;Pidgeon, 1970;Hanushek, 1986;Reimers & McGinn, 1997;Snow, 1998;Darling-Hammond, 2000), and the curriculum (Phillips, 1997;Howard et al., 1999;Cohan, 1994). Some reasons cited for the ambiguity are the methodologies, imprecision, and resistance of existent structures to change. ...
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While improving performance and efficiency in educational production has been the concerned of educators, social scientists, and politicians for decades, questions such as how to improve and how to measure performance and efficiency still remain. Analysis of an educational production focusing on improving and controlling its performance and efficiency leads to a modeling process whose main goal is to increase our understanding of its structure and dynamics. The core to this modeling process is model completeness, which deals with a description of the system or problem being modeled and the resolution of uncertainties. Satisfaction of model completeness is a critical requirement to improve model accuracy and resolution. This, however, is a portentous task when dealing with dynamics and complex systems like educational production. This work addresses the issue of satisfying completeness in the formalization of a descriptive model of a K-12 educational production system. By examining a series of concepts and problems, we bring into shaper focus features characterizing the system complexity. Describing this system, including functions and objectives, variables, requirements, and the input-output functional relationships, requires large amount of information, which is often imprecise. Thus it is difficult, perhaps impossible, to resolve the uncertainties. This complexity constrains the development of models that can effectively support decision-making. Hence, complexity management becomes a critical requirement of a modeling process that seeks to increase completeness.
Thesis
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Concepts such as "quality", "effectiveness", "efficiency", "quality control", and "evaluation criteria" hold a central position in the educational sphere over the last years. These concepts mainly stem from the domains of economy and businesses, where they are linked to the objective of increasing the efficiency of modern competitive production units. Lastly, we observe that their impact is extended to the educational area, where they are used as a vehicle to formulate strategies and methodologies for the development of modern educational systems. The contribution of information and communication technologies (ICT) to the evolution of education to date, has been approached mainly in terms of learning-educational results, while the relevant research literature internationally focuses on the pedagogical, psychological and sociological impact of technology and other related forms of teaching in a digitally transformating educational environment. It is relatively rare that research efforts focus on the economic evaluation of the contribution of ICTs, by exploring the effectiveness or efficiency of the training providers, the costs and benefits for the participants, or the overall impact on the surrounding learning environment. Therefore, this study has a dual purpose: on the one hand, we attempt to record, present, analyze and correlate the educational costs of secondary schools with their degree of effectiveness in a critical comparative context, through a customized Cost-Effectiveness Analysis methodology, deploying a representative sample of 30 school units, and on the other hand, we attempt to validate, through an empirical research design, a complex pre-existing theoretical model of total quality improvement of the secondary education, that proposes certain factors of quality and evaluation criteria for them. In this direction, we attempt, via a sample of 512 secondary school teachers, to investigate the extent to which teachers' attitudes towards ICT influence their views on the importance of other model factors in improving the quality of education. Regarding the data collection method used, we chose the exploratory and productive approach. An extended bibliography overview was held, in the field of economic evaluation of educational programs, where the approaches proposed by the researchers were studied, and on the other hand the role of technology in the improvement of quality of education was studied, as well as the main problems involved in such an approach were taken into consideration. The research results revealed that the educational costs of a secondary school unit do not significantly affect the degree of ICT use in it. Also, the type of school (public vs private) was not found to affect the amount of educational costs of a secondary school unit. Finally, it was found that teachers' attitudes towards ICT do not affect their opinion about other factors that contribute to the improvement of quality of education. The results can be used as valuable scientific aid by the researchers who are interested in the issues of administration and organization of education, as well as in the promotion of educational quality at multiple levels of analysis.
Article
This paper reviews the analyses of the prevailing paradigm in administration and economics in their approach to education. Deriving from these investigation lines, some proposals were created for changes in the regulation and assignment of resources to education. These proposals, founded on the lack of financial support to enhance quality, show some persistence on mechanisms that range from decentralized strategies to total mercantilization. In the first case, some mechanisms are created to attract different kinds of public, but for different reasons and with different kinds of reach. In the second case, State action would be limited to the establishment of a few rules.
Article
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This paper reviews the analyses of the prevailing paradigm in administration and economics in their approach to education. Deriving from these investigation lines, some proposals were created for changes in the regulation and assignment of resources to education. These proposals, founded on the lack of financial support to enhance quality, show some persistence on mechanisms that range from decentralized strategies to total mercantilization. In the first case, some mechanisms are created to attract different kinds of public, but for different reasons and with different kinds of reach. In the second case, State action would be limited to the establishment of a few rules.
Article
Political scientists have widely employed production function models as tools for theory confirmation and policy prescription. Although an important part of a growing literature within the discipline, production function research frequently produces contradictory results, an inconsistency that raises questions about the role of normative preferences in quantitative analysis. In this article we seek to explain the variation in the empirical results of production functions research in education. While recognizing normative values may have some influence in research, we argue this can be minimized if the conceptual and methodological weaknesses inherent in applying production function logic to the public sector are recognized and addressed.
Article
This article advances a theory of educational productivity based on a paradigm of classroom diversification that defines a strategic view of the education production process. The paradigm's underlying premise is that classroom student performance, and the instructional interactions that produce such outcomes, depend on economies derived from the learning relationships that exist across and among students in a classroom and on the technological fit between students' learning needs and a teacher's capacity. In addition to the conceptual classroom diversification framework, measures of classroom student diversity and teacher capacity are presented, followed by a discussion of the implications of the proposed classroom diversification paradigm for educational research, policy, and practice.
Article
To identify the fittest quantity for every higher education resources in Heilongjiang province, a surface model is constructed based on collected data in 20 years, 15 vectors and the corresponding multinomial equation. Firstly, the vectors are integrated to human capital, material capital, intellectual capital and intangible capital, which have been reconstructed from the original data. Considering the performance of teaching and studying respectively, an integrated one is get to make the dependence variable, and the corresponding parameters are get by least square method. At last, joint analyzing the factual situation of Heilongjiang Province's high education resource, the fittest resources are adjusted from the quantity get by the model.
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In one of the largest studies yet carried out on the subject, the average scores on state-developed and nationally standardized tests of third-, sixth-, and ninth-graders in New Jersey districts were regressed on indexes of district socioeconomic status (SES), per-student expenditures on education, and the size of enrollments in the districts. The numbers of districts entering the analyses, depending on grade level and test, varied from 261 to 507. SES accounted for much of the accountable variance; higher SES districts, of course, achieved more than lower SES districts. When SES was taken into account, higher expenditures were inconsistently and generally insignificantly (probability less than 0. 05) associated with lower test scores; and students m smaller districts generally achieved more than those in larger districts. The inefficiency of expenditures and diseconomies of scale in rinsing achievement are contrary to popular and considerable opinion but corroborate previous research.
Article
Studies analyzing expenditures for public education have used a variety of inputs into the educational process as proxies for the quality of education. This study attempts to isolate some of the inputs which do, in fact, have an effect upon educational quality. To accomplish this, output measures of quality were derived from a sample of 5,000 West Virginia University students who had graduated from high schools within the state. The results show that only one of the input variables examined, teachers' salaries, was significantly related to the output measures of quality. In addition, factors exogenous to the local school system-factors reflecting socioeconomic characteristics of the communities in which the school systems were located-were observed to have a significant effect upon quality. The results give rise to dual conclusions. First, input variables seem to be imprecise measures of educational quality. Second, the empirical evidence provides some support for the contention that the quality of education may be improved by offering higher salaries to teachers.
Article
This article begins with a critical review of alternative strategies currently in use to study educational productivity. These unfolding research programs are considered in the light of increasing public demands for improvement of productivity in education. A critique is offered of the dominant conception of the education production process that undergirds many of these studies, and alternative conceptions are offered. The effects of efforts to improve productivity are examined in the context of each of these different conceptions. The article concludes by advocating a new line of research designed to generate insight into more fundamental aspects of education production processes. This new type of productivity research places greater emphasis than is customary on the classroom as the unit of analysis.
Article
The mathematics achievement scores of 28,274 students in 1443 Australian, Belgian, English, Finish, French, German, Israeli, Japanese, Dutch, Scotch, Swedish, and U.S. elementary schools were correlated with, and regressed on socioe‐conomic status, highest math course taken, weekly hours of homework, interest in mathematics, and several other variables with both individuals and schools within each country as units of analysis. The results corroborate recent syntheses of small‐scale studies of productive factors in academic learning as well as regression analyses of large‐scale surveys. Among directly alterable variables, the amount and the quality or vigour of instruction including homework most strongly influence achievement.