
1. INTRODUCTION
In 1989, the Nation's President along with its governors made
clear that there was a keen interest in comparing the educational
performance of United States' students with that of students in
other countries. That year a National Education Summit adopted
six education goals, one of which stated that by the year 2000,
"U.S. students will be first in the world in science and mathematics
achievement" (National Education Goals Panel, 1991, p. 16).
The Third International Mathematics and Science Study (TIMSS),
conducted in 1995, provides the most recent information about
our country's progress toward this goal. The U.S. TIMSS results
describe student mathematics and science achievement for several
grades (including grades 4, 8, and 12) both for the country as
a whole and for various subgroups of the population. These U.S.
results are directly comparable to TIMSS results from many other
countries. However, with the exception of a few states that chose
to participate in the statelevel TIMSS program, equivalent TIMSS
results are not available at the state level.
Because education in the United States is largely determined at
the state and local levels, there has been considerable interest
in how the performance of students in individual states compare
with each other, with the United States, and with other nations. The comparison of state performance
with other states and with the United States is made possible by the National Assessment of Educational Progress
(NAEP). In 1996, NAEP assessed mathematics and science in the
United States as a whole. Additionally, results for the individual states that
chose to participate in the state NAEP assessment are available
at grades 4 and 8 for mathematics and at grade 8 for science.
Thus, while it is directly possible to compare the participating
states with each other and with the United States, policymakers and the general public cannot directly know how
the students in the various states would perform relative to students
in other countries.
Since TIMSS and NAEP were administered within a year of each other,
there has been considerable interest in attempting to link the
two assessments. Such a linkage would, for example, allow states
who participated in the state component of the NAEP mathematics
or science assessments to compare their predicted TIMSS results
with results from countries participating in TIMSS. Specifically,
predicted means on TIMSS could be estimated for each state that
participated in NAEP, with the prediction based on an application
of a linking function to that state's NAEP data. Additionally,
the percentages of students in the states who would score above
selected points on the TIMSS scale, such as the international
marker levels, had they participated in the TIMSS assessment,
could be predicted from their NAEP proficiency distributions based
on a linking function.
The success of the link between the 1992 NAEP mathematics results
with those from the 1991 International Assessment of Educational
Progress (IAEP) in mathematics (Pashley and Phillips 1993) provided
encouragement that a link between TIMSS and NAEP was possible.
The purpose of this report is to describe the methods used to
undertake such a link using the available data. The specific direction
of the link will be to link NAEP to TIMSS, thereby providing predicted
TIMSS results for given NAEP results. Since a major goal of the
link is to enable comparisons between states and countries, links
were intended to be established for those grades and subjects
where there are both state NAEP data and international TIMSS data.
The links were to be based on the data from the U.S. TIMSS national
sample and from the NAEP national sample. The linkages provided
in this report are for mathematics and science at grade 8. An
additional link is being attempted for grade 4 mathematics but
is still undergoing NCES review.
While developing the links is straightforward, the real challenge
is in identifying the various sources of error that are associated
with linking together two assessments and in developing components
of variance attributable to as many of these as is possible. This
report estimates components of variance due to four sources: (1)
sampling, (2) measurement error, (3) model misspecification, and
(4) temporal shift. These components are used to derive standard
errors for predicted TIMSS state means and percentages and then
used to construct confidence intervals around these estimates
for each state.
The quality of the link between NAEP and TIMSS was evaluated using
data from the states for whom representative data were available
from both assessments. Specifically, the predicted TIMSS results,
based on the state's NAEP data, were compared with the actual
results for the state. In the 1995 administration of TIMSS, one
state, Minnesota, elected to participate in the grade 8 TIMSS
assessments of mathematics and science. As is shown in this report,
the predicted results for that state are quite close to the actual
results for the grade 8 mathematics and science assessments. In
addition, two states, Missouri and Oregon, participated in a special
assessment of the TIMSS in their states in 1997. While the results
of these assessments have not yet been publicly released, the
predicted TIMSS results for these states were consistent (within
acceptable statistical bounds) with their actual TIMSS results.
This is heartening, since as discussed in the next section, the
type of linking required for the available data requires caution
in its use. Based on a number of studies, the moderation type
of linking, as is used in this report, is adequate for the approximate
comparisons of the relative rankings of individual states versus
other countries, but is likely not adequate for extensive analyses
based on the point estimates of scores.
