Small sample tests for the equality of intraclass correlation coefficients under unequal family sizes

Large sample tests have been proposed for testing the equality of two or three intraclass correlation coefficients when the family sizes are unequal. The theoretical developments of these tests can be found at Young and Bhandary (1998) and Bhandary and Alam (2000). In this research, we focus on the case when the sample size is very small. First, we consider a case with two populations. The exact null distribution of the test statistic is derived. We use a Monte Carlo simulation study and find that the performance of our new test is superior to the tests that were proposed by Young and Bhandary (1998). Work is then extended to develop a test for three intraclass correlation coefficients. We use Bonferroni's approach to approximate the critical value at a specified alpha level for testing the equality of intraclass correlation coefficients. We propose several possible critical regions based on different measures. Simulation studies are conducted to investigate which choice of these three critical regions is the most appropriate for our new test. We compare our new test and the test that was proposed by Bhandary and Alam (2000) and recommend our new test in practice when the sample sizes are small.