An Exact Test for the Equality of Intraclass Correlation Coefficients Under Unequal Family Sizes

Abstract

An exact test for the equality of two intraclass correlation coefficients under unequal family sizes based on two independent multi-normal samples is proposed. This exact test consistently and reliably produced results superior to those of the Likelihood Ratio Test (LRT) and the large sample Z-test proposed by Young and Bhandary (1998). The test generally performed better in terms of power (for higher intraclass correlation values) for various combinations of intraclass correlation coefficient values and the exact test remained closer to the significance level under the null hypothesis compared to the other two tests. For small sample situations, sizes of the LRT and large-sample Z-tests are drastically higher than alpha-level, but the size of the exact test is close to the alpha-level. The proposed exact test is computationally simple and can be used for both small and large sample situations.