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ERIC Number: EJ848306
Record Type: Journal
Publication Date: 2004
Pages: 31
Abstractor: As Provided
Reference Count: 35
ISSN: ISSN-0211-2159
Inflation of Type I Error Rates by Unequal Variances Associated with Parametric, Nonparametric, and Rank-Transformation Tests
Zimmerman, Donald W.
Psicologica: International Journal of Methodology and Experimental Psychology, v25 n1 p103-133 2004
It is well known that the two-sample Student t test fails to maintain its significance level when the variances of treatment groups are unequal, and, at the same time, sample sizes are unequal. However, introductory textbooks in psychology and education often maintain that the test is robust to variance heterogeneity when sample sizes are equal. The present study discloses that, for a wide variety of non-normal distributions, especially skewed distributions, the Type I error probabilities of both the t test and the Wilcoxon-Mann-Whitney test are substantially inflated by heterogeneous variances, even when sample sizes are equal. The Type I error rate of the t test performed on ranks replacing the scores (rank-transformed data) is inflated in the same way and always corresponds closely to that of the Wilcoxon-Mann-Whitney test. For many probability densities, the distortion of the significance level is far greater after transformation to ranks and, contrary to known asymptotic properties, the magnitude of the inflation is an increasing function of sample size. Although nonparametric tests of location also can be sensitive to differences in the shape of distributions apart from location, the Wilcoxon-Mann-Whitney test and rank-transformation tests apparently are influenced mainly by skewness that is accompanied by specious differences in the means of ranks. (Contains 4 tables and 10 figures.)
University of Valencia. Dept. Metodologia, Facultad de Psicologia, Avda. Blasco Ibanez 21, 46010 Valencia, Spain. Tel: +34-96-386-4100; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A