RAW-SCORE CONDITIONAL STANDARD ERRORS OF MEASUREMENT IN GENERALIZABILITY THEORY

A comprehensive, integrated treatment is provided of both conditional absolute (Delta-type) standard errors of measurement (SEM) and conditi onal relative (delta-type) SEMs from the perspective of generalizabili ty theory. Results are provided for univariate single-facet designs, m ultivariate single-facet designs, and designs with multiple random fac ets. Some previously derived conditional SEMs are shown to be special cases of results derived here. Average values (over examinees) of cert ain conditional SEMs are shown to be related to the error variances in coefficient alpha and stratified alpha. It is shown that the conditio nal Delta-type SEM is the standard error of the mean for the within-pe rson design. As such, it is unaffected by the across-persons design an d relatively easy to estimate. By contrast, the conditional delta-type SEM is necessarily influenced by the across-persons design and often quite complicated to estimate, especially for multifacet designs. Almo st all estimators are illustrated with data from the Iowa Tests of Bas ic Skills, the Iowa Tests of Educational Development, the Iowa Writing Assessment, and the QUASAR project. These examples support the conclu sion that both types of conditional SEMs tend to be smaller at the ext remes of the score scale than in the middle. Further, these examples s uggest that a concave-down quadratic function fits the estimates quite well in a wide variety of cases.