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

Abstract

The eta-squared (TI 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, TI 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 ~2 is described, and a simulation verifying the relationship between group size and 112 is conducted. The simulation demonstrates the conditions under which T] 2 does and does not provide a biased estimate of group-level properties. The paper concludes by (a) discussing corrections for 1"12, and (b) providing guidelines for calculating estimates of group-level properties in samples having unequal group sizes. The analysis of group-level data has received considerable attention in orgaA key concern in group-level analyses is the need to determine how much (if any) of a variable's total variance is due to the group-level properties of the data. This issue is important because the amount of the total variance that is due to the group-level properties of the data has theoretical implications about underlying group processes. Strong Underlying group processes are assumed to be reflected in data that have strong group-level properties, while weak underlying group processes are assumed to correspond to weak group-level properties (Dansereau, et al., 1984;James, 1982).One approach commonly used to estimate the magnitude of the group-level properties of data is based on a one-way random effects ANOVA model. In the ANOVA model, the variable of interest is predicted from a group membership factor. For example, one might conduct an analysis in which individual percep-

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