Sampling Characteristics of Kelley's ε and Hays' ω

Abstract

Statistics used to estimate the population correlation ratio were reviewed and evaluated. The sampling distributions of Kelley's ε² and Hays' ω² were studied empirically by computer simulation within the context of a three level one-way fixed effects analysis of variance design. These statistics were found to have rather large standard errors when small samples were used. As with other correlation indices, large samples are recommended for accuracy of estimation. Both ε² and ω² were found to be negligibly biased. Heterogeneity of variances had negligible effects on the estimates under conditions of proportional representativeness of sample sizes with respect to their population counterparts, but combinations of heterogeneity of variance and unrepresentative sample sizes yielded especially poor estimates.

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