A Small Sample Test for the Equality of Intraclass Correlation Coefficients Under Unequal Family Sizes for Several Populations

Abstract

A small sample test for the equality of several intraclass correlation coefficients under unequal family sizes based on several independent multinormal samples has been proposed. It has been found that the small sample test consistently and reliably produced results superior to those of likelihood ratio test (LRT) proposed by Bhandary and Alam (2000) in terms of power most of the times (for higher intraclass correlation values for various combinations of intraclass correlation coefficient values and also the small sample test stays closer to the significance level under null hypothesis compared to the likelihood ratio test.

For small sample situation, LRT has size drastically different from alpha-level whereas, the small sample test gives size closer to the alpha-level. This small sample test is computationally very simple and also can be used for both small sample and large sample situations. An example with real life data is presented.

Keywords:

• F _max-test
• Intraclass correlation coefficient
• Likelihood ratio test

Mathematics Subject Classification:

• 62H15
• 62H10

Acknowledgments

The authors would like to thank the referee for very careful reading of this manuscript and the suggestion of simulation of larger size and other important comments which improved the quality of this manuscript and broaden its content.