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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 state-level 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.