The test of homogeneity for intraclass correlation coefficients has been one of the active topics in statistical research. Several chi-square tests have been proposed to test the homogeneity of intraclass correlations in the past few decades. The big concern for them is that these methods are seriously biased when sample sizes are not large. In this thesis, data driven approaches are proposed to testing the homogeneity of intraclass correlation coefficients of several populations. Through simulation study, data driven methods have been proved to be less biased and accurate than some commonly used chi-square tests.