Inflation of type I error rates by unequal variancesassociated with parametric, nonparametric, andRank-Transformation Tests
Year: 2004
Type: article
Abstract: "It is well known that the two-sample Student t test fails to maintain itssignificance level when the variances of treatment groups are unequal, and,at the same time, sample sizes are unequal. However, introductory textbooksin psychology and education often maintain that the test is robust to varianceheterogeneity when sample sizes are equal. The present study discloses that,for a wide variety of non-normal distributions, especially skeweddistributions, the Type I error probabilities of both the t test and theWilcoxon-Mann-Whitney test are substantially inflated by heterogeneousvariances, even when sample sizes are equal. The Type I error rate of the ttest performed on ranks replacing the scores (rank-transformed data) isinflated in the same way and always corresponds closely to that of theWilcoxon-Mann-Whitney test. For many probability densities, the distortionof the significance level is far greater after transformation to ranks and,contrary to known asymptotic properties, the magnitude of the inflation is anincreasing function of sample size. Although nonparametric tests of locationalso can be sensitive to differences in the shape of distributions apart fromlocation, the Wilcoxon-Mann-Whitney test and rank-transformation testsapparently are influenced mainly by skewness that is accompanied byspecious differences in the means of ranks."
Author: Donald W. Zimmerman
Institution: Universitat de València
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2169502209