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Vol. 13 No. 2 (2023)
Education and Social Studies

Articles

Parametric Alternatives to the Student T Test under Violation of Normality and Homogeneity of Variance

Published 2024-08-25

  • Donald W. Zimmerman
    • ,
  • Bruno D. Zumbo

Donald W. Zimmerman
Carleton University

Bruno D. Zumbo
University of Ottawa

Abstract

Introductory statistics textbooks in psychology, education, and social sciences have contributed to the belief that nonparametric tests, such as the Wilcoxon-Mann-Whitney test, are effective against violations of both normality and homogeneity of variance. The present paper emphasizes that, although rank methods often are useful when samples are obtained from heavy-tailed, nonnormal distributions, they are influenced by unequal variances just like parametric tests. Computer programs are now available to perform modified t tests based on unequal sample variances, in which degrees of freedom and critical values are altered from sample to sample. These procedures, although neglected for many years because they are computationally complex, are far more effective than nonparametric methods in protecting against violation of homogeneity of variance.

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