The relationship between variance components and mean difference effect size

Abstract

Variance components in the context of Generalizability Theory are useful indices for attributing the amount of variance to a particular facet or object of measurement. The mean difference effect size (MDES) has proven to be a useful tool both in synthesizing the results of multiple studies and in interpreting individual study results. A mathematical relationship is drawn, therefore, between the variance components of a nested two-facet design configuration on the one hand, and the MDES that can be calculated from the descriptive statistics of an hypothetical measurement study on the other. Using two different variance components estimation procedures, we show that the relationship is both statistically and conceptually meaningful in that all of these estimates closely approximates the true Glassian MDES.