Robustness of normal theory inference when random effects are not normally distributed

Abstract

The variance of a response in a one-way random effects model can be expressed as the sum of the variability among and within treatment levels. Conventional methods of statistical analysis for these models are based on the assumption of normality of both sources of variation. Since this assumption is not always satisfied and can be difficult to check, it is important to explore the performance of normal based inference when normality does not hold. This report uses simulation to explore and assess the robustness of the F-test for the presence of an among treatment variance component and the normal theory confidence interval for the intra-class correlation coefficient under several non-normal distributions. It was found that the power function of the F-test is robust for moderately heavy-tailed random error distributions. But, for very heavy tailed random error distributions, power is relatively low, even for a large number of treatments. Coverage rates of the confidence interval for the intra-class correlation coefficient are far from nominal for very heavy tailed, non-normal random effect distributions.