Some Empirical Results on Variance Ratios under Permutation in the Completely Randomized Design

Abstract

Normal theory and permutation bases exist for the variance ratio tests employed in the analysis of randomized experiments. Analytic and empirical evidence indicates good agreement of the probability of a Type I error and of power for variance ratio tests under these two bases. The agreement is, however, affected by the properties of the basic data which are permuted. In the present study, basic data sets possessing various combinations of skewness, kurtosis, and number of observations were employed to study the effects of these factors upon this demonstrated agreement. The empirical results indicate that for the completely randomized design the agreement of either size or power under these two bases is good over a reasonable range of skewness and kurtosis of the basic data. Only extremely leptokurtotic basic data sets affect this agreement and this can be offset somewhat by increased sample size.