Three tests are proposed based on F-distribution, Likelihood Ratio Test (LRT) and large sample Z-test for intraclass correlation coefficient under unequal family sizes based on a single multinormal sample. It has been found that the test based on F-distribution consistently and reliably produces results superior to those of Likelihood Ratio Test (LRT) and large sample Z-test in terms of size for various combinations of intraclass correlation coefficient values. The power of this test based on F-distribution is competitive with the power of the LRT and the power of Z-test is slightly better than the powers of F-test and LRT when k = 15, but the power of Z-test is worse in comparison with the F-test and LRT for k = 30, i.e. for large sample situation, where k = sample size. This test based on F-distribution can be used for both small sample and large sample situations. An example with real data is presented.
Bhandary, Madhusudan and Fujiwara, Koji
"Test for Intraclass Correlation Coefficient under Unequal Family Sizes,"
Journal of Modern Applied Statistical Methods: Vol. 12
, Article 9.
Available at: http://digitalcommons.wayne.edu/jmasm/vol12/iss2/9