Testing intraclass correlation coefficients

Abstract

One-sided, two-sided unbiased and likelihood ratio tests for testing the equality of intraclass correlations for two multivariate normal populations are studied in detail in respect of the computational methods for constructing tables of critical values. By simulations it is shown that the likelihood ratio test for testing the equality of two intraclass correlations for unequal p₁ and p₂ variates normal populations depends on the nuisance parameter ρ, the common intraclass correlation under H₀ when the sample sizes are small. The one degree of freedom chisquare approximation to the likelihood ratio test statistic is sufficiently accurate for all values of ρ when sample sizes are over 20, and could be used in practice even in small samples although it overestimates significance.