Heterogeneity of variance and biased hypothesis tests

Donald W. Zimmerman

Journal of Applied Statistics, 2013, vol. 40, issue 1, 169-193

Abstract: This study examined the influence of heterogeneity of variance on Type I error rates and power of the independent-samples Student's t -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 biased , so that under some conditions, the probability of rejecting H 0 decreased as the difference between means increased. In all cases where bias occurred, the t -test on ranks exhibited substantially greater bias than the t -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.

Date: 2013
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DOI: 10.1080/02664763.2012.740620

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