Test for equality of intraclass correlation coefficients under unequal family sizes

The likelihood ratio test, the large-sample z-test, and the large-sample z-test have been proposed to test for the equality of two intraclass correlation coefficients under unequal family sizes based on two independent multinomial samples. It has been found on the basis of simulation studies that the likelihood ratio test consistently and reliably produces results superior to those of the large-sample z-test and large-sample z-test in terms of power for various combinations of intraclass correlation coefficient values.