Confidence Intervals and F Tests for Intraclass Correlations Based on Three-Way Random Effects Models

Abstract

This article gives equations for computing confidence interval estimates and conducting F tests for intraclass correlation coefficients (ICCs) defined using three-way random effects models for crossed and nested designs. The estimates and tests employ mean squares from analyses of variance. The equations are generalized so that data from an initial pilot study (G study) can be used to prophesy the confidence limits for ICCs in data with more or fewer factor levels. Equations also are included for determining the optimal number of factor levels to use in a design that will offer confidence of 1-[.alpha] that the population ICC is equal to or exceeds a fixed lower limit.