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APPENDIX F: Deriving the Effectiveness
Index
The Effectiveness Index (EI) is derived
by comparing actual scores on standardized tests with
scores as predicted by a model which factors in the
role community characteristics play in educational outcomes.
The Community Effects Factor (CEF)
model was developed in a doctoral
dissertation (Education Achievement Communities: A New
Model for "Kind of Community" in Massachusetts
Based on an Analysis of Community Characteristics Affecting
Educational Outcomes, May 1998, University of Massachusetts,
Amherst). That work is the basis for determining school
effectiveness. The model examines the relationship between
selected demographic characteristics and educational
outcomes. These characteristics include: average education
level, average income, poverty rate, single-parent status,
language spoken, and percentage of school-age population
enrolled in private schools. These variables were chosen
because they correlate with achievement and because
the education literature identifies them as connected
to academic performance.
In order to refine a better CEF model,
it is first necessary to factor the impact of these
demographic variables on each other. This can be done
through a technique known as principal components analysis
that is a statistical mechanism that reduces many variables
to a few salient ones that have the most impact on an
outcome. Once the factors have been identified, a regression
analysis produces the equations that can be used to
either build a kind-of-community model or to predict
expected district
performance on achievement tests. The degree to which
a community's characteristics lifts or lowers test scores
is reflected in a Community Effects Factor (CEF), a
measure of demography.
The CEF, which is a measure of the
demographic lift or drag of each community concerning
educational achievement, is a good point of departure
for analyzing school and school district effectiveness.
The CEF identifies expected levels of performance based
on community characteristics which, for better or worse,
are very powerful indicators of educational achievement
in Massachusetts. In this analysis, Weston is the most
demographically advantaged community in the state in
terms of educational outcomes (CEF = + 2.8), and Lawrence
is the least advantaged (CEF = - 4.8). The CEF has a
strong relationship, or correlation, to test scores.
Correlation is a process that identifies
the interdependence of one variable with another. Correlation
simply shows "the extent to which two things typically
run together." [The Economist, 6 Dec. 1997, p.
82]. Correlation is not equivalent to causation; it
can only reveal tendencies between variables, not identify
causes. Correlations simply demonstrate relationships.
A perfect correlation would be 1.0. For example, the
correlation between inches and feet is 1.0 because it
is a perfect linear fit; 12 inches always equals one
foot. Correlations in real world situations involving
human behavior are never 1.0.
The correlation, or the connection,
between spending (Per-Pupil Expenditure or PPE) and
achievement in Massachusetts is relatively low. While
spending clearly matters, merely increasing spending
levels has a relatively weak impact on results. Increasingly,
many people are coming to the realization that how a
system spends money is more important than how much
money it spends. The achievement outcome accounted for
by the community effects factor (CEF) is much stronger;
that relationship is .83. This is not to say the community
context, the CEF, is the most important determinant
of school success, but it is a significant element that
must be a major consideration in any plan to improve
education in disadvantaged areas.
The Effectiveness Index (EI) is generated
in the following manner:
• · Utilize the 1998 MCAS
results as an outcome indicator for achievement in
each of the state's most populous 240 or so districts
(the exact number depends on grade level). (NOTE: This
model does not evaluate results in the smallest communities
of the state which comprise about 2% of the population.)
• · Utilize the EI model
to predict a score for each district. This
predicted score is based solely on community characteristic
as they affect
educational outcomes.
• · Compare the actual to
the predicted score. Systems whose actual scores
are significantly higher than predicted scores and whose
absolute scores are at or above state average are identified
as Effective. Systems with positive effectiveness indexes
but scores below state average are identified as Noteworthy.
The basis for this model was developed
as a doctoral dissertation. The following provides detail
on the statistics behind the model which is used to
predict expected scores based on demographics.
Robert D. Gaudet
rgaudet@rnc.com
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