On testing equality of intraclass correlations under unequal family sizes

The three likelihood-based tests, namely, likelihood ratio test, Rao score test, and Wald test and two more asymptotic tests which use Srivastava's estimator of intraclass correlation coefficient are considered to test the null hypothesis of equality of intraclass correlation coefficients when the families have unequal number of children. Methods are illustrated on Galton's data set. Using simulation experiment we compute the sizes and powers of these tests and compare. It is found that our proposed test using Srivastava's estimator and the score test perform the best among all tests.