Group Size and Measures of Group-Level Properties: An Examination of Eta-Squared and ICC Values

Abstract

The eta-squared (η 2 ) from a one-way random effects ANOVA is an index commonly used to estimate group-level properties of data in multilevel research. Under some circumstances, however, η 2 values provide biased estimates of the group-level properties. Biased estimates occur because the magnitude of the 1.12 in a one-way rando m effects ANOVA is partially a function of group size. In this paper, the relationship between group size and η is described, and a simulation verifying the relationship between group size and 112 is conducted. The simulation demonstrates the conditions under which η does and does not provide a biased estimate of group-level properties. The paper concludes by (a) discussing corrections for η 2 , and (b) providing guidelines for calculating estimates of group-level properties in samples having unequal group sizes.