Existing theoretical and empirical evidence indicates that, except for small samples, the null and non-null distributions of the variance ratios involved in the analysis of the randomized block design, based upon normal theory agree reasonably well with those under permutation theory. The present paper investigated the combined effect of block-treatment interaction and block-variance heterogeneity upon this agreement. Using a normal theory α cut-off point, the empirical probability of type I error under a permutation basis was markedly reduced by this combination of factors, and empirical power was also reduced. Additionally, the combined effect of kurtosis and block-variance heterogeneity was studied. The results indicated that kurtosis of the basic data had negligible effect upon either the null or non-null distribution of the variance ratios involved.