Consequences of choosing samples in hypothesis testing to ensure homogeneity of variance

The two-sample Student t test of location was performed on random samples of scores and on rank-transformed scores from normal and non-normal population distributions with unequal variances. The same test also was performed on scores that had been explicitly selected to have nearly equal sample variances. The desired homogeneity of variance was brought about by repeatedly rejecting pairs of samples having a ratio of standard deviations that exceeded a predetermined cut-off value of 1.1, 1.2, or 1.3, while retaining pairs with ratios less than the cut-off value. Despite this forced conformity with the assumption of equal variances, the tests on the selected samples were no more robust than tests on unselected samples, and in most cases substantially less robust. Under conditions where sample sizes were unequal, so that Type I error rates were inflated and power curves were atypical, the selection procedure produced still greater inflation and distortion of the power curves.