The sampling distribution of the ANOVA estimator of the between group variances component in a balanced one-way random effects model, where samples for both the random effects are from Edgeworth population, is derived and is shown to be quite sensitive to the kurtosis of random effects. A chi-square approximation to the exact distribution is proposed and shown to be quite accurate. Numerical results are presented and graphically displayed to highlight the effects of departure from normality. Confidence intervals for the between variance component are constructed and are found to be too wide for positive kurtosis of the group effects.
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