Theorems already enunciated in a previous paper on quadratic forms are used to determine the effects of inequality of variance and first order serial correlation of errors in the two-way classification on the analysis of variance. It is found that when the appropriate null hypothesis is true, inequality of variance from column to column results in an increased chance of exceeding the significance point for the test on homogeneity of column means, and a decreased chance for the corresponding test on row means. For moderate differences in variance neither effect is large. First order serial correlation within rows produces a large effect on the "between rows" comparisons, but little effect on the "between columns" comparisons.
G. E. P. Box. "Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, II. Effects of Inequality of Variance and of Correlation Between Errors in the Two-Way Classification." Ann. Math. Statist. 25 (3) 484 - 498, September, 1954. https://doi.org/10.1214/aoms/1177728717