Although the component for model misspecification was tested to be equal to zero, there is still some minor, albeit nonsignificant, difference in results between a link based on students in all schools and that based on public schools only. Since the major reporting aim of the link was to relate state results from the State NAEP to country results from TIMSS, since the published NAEP State results pertain to public school students only, and since the TIMSS private school samples were small and unstable, it was appropriate to use the public school data for this purpose.
The parameters used for linking public school State NAEP results to TIMSS are shown in Table 11. Table 12 provides the components of the variance of the linked estimate from Equation (5). These components include the variances due to sampling, measurement error, and temporal shift. Each of these variances was computed in the manner described in previous sections, with the exception that all computations were based on the data from public school students only.