Raw-Score Conditional Standard Errors of Measurement in Generalizability Theory

Abstract

A comprehensive, integrated treatment is provided of both conditional absolute (A-type) standard errors of measurement (SEM) and conditional relative (a-type) SEMs from the perspective of generalizability theory. Results are provided for univariate singlefacet designs, multivariate single-facet designs, and designs with multiple random facets. Some previously derived conditional SEMs are shown to be special cases of results derived here. Average values (over examinees) of certain conditional SEMs are shown to be related to the error variances in coefficient a and stratified a. It is shown that the conditional A-type SEM is the standard error of the mean for the within-person design. As such, it is unaffected by the across-persons design and relatively easy to estimate. By contrast, the conditional 8-type SEM is necessarily influenced by the across-persons design and often quite complicated to estimate, especially for multifacet designs. Almost all estimators are illustrated with data from the Iowa Tests of Basic Skills, the Iowa Tests of Educational Development, the Iowa Writing Assessment, and the QUASAR project. These examples support the conclusion that both types of conditional SEMs tend to be smaller at the extremes of the score scale than in the middle. Further, these examples suggest that a concave-down quadratic function fits the estimates quite well in a wide variety of cases.