Sample size determination in the Mann–Whitney test

Andrzej Kornacki 1 , Andrzej Bochniak 1  und Agnieszka Kubik-Komar 1
  • 1 Department of Applied Mathematics and Computer –Science, University of Life Sciences in Lublin, Akademicka 15, 20-950 , Lublin, Poland


This paper discusses the problem of determining the number of observations necessary to apply the nonparametric Mann-Whitney test. We describe the method given by Noether (1987) for determining a sample size which guarantees that the Mann-Whitney test at a given significance level α has a predetermined power 1-β. The presented theory is tested by calculating the empirical power in computer simulations. The paper also raises the issue of the method of rounding the determined sample size to an even number when the sample is divided into two equinumerous subsamples.

Falls das inline PDF nicht korrekt dargestellt ist, können Sie das PDF hier herunterladen.

  • Cohen, J. (1988) Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

  • Cohen, J. (1992) A power primer. Psychological Bulletin, Vol 112(1), 155-159.

  • Fisz M. (1967) Rachunek Prawdopodobieństwa i Statystyka Matematyczna. PWN, Warsaw.

  • Hamedani, G. G.; Tata, M. N. (1975) On the determination of the bivariate normal distribution from distributions of linear combinations of the variables. The American Mathematical Monthly, 82 (9): 913-915.

  • Noether G. E. (1987) Sample Size Determination for Some Common Nonparametric Tests. Journal of the American Statistical Association 82: 645-647.


Zeitschrift + Hefte