Heterogeneity of variance and biased hypothesis tests
This study examined the influence of heterogeneity of variance on Type I error rates and power of the independent-samples Student's <italic>t</italic>-test of equality of means on samples of scores from normal and 10 non-normal distributions. The same test of equality of means was performed on corresponding rank-transformed scores. For many non-normal distributions, both versions produced anomalous power functions, resulting partly from the fact that the hypothesis test was <italic>biased</italic>, so that under some conditions, the probability of rejecting <italic>H</italic> <sub>0</sub> decreased as the difference between means increased. In all cases where bias occurred, the <italic>t</italic>-test on ranks exhibited substantially greater bias than the <italic>t</italic>-test on scores. This anomalous result was independent of the more familiar changes in Type I error rates and power attributable to unequal sample sizes combined with unequal variances.
