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Optimal sample size planning for the Wilcoxon-Mann-Whitney test.

Martin Happ1, Arne C Bathke1,2, Edgar Brunner1,3

  • 1Department of Mathematics, University of Salzburg, Salzburg, Austria.

Statistics in Medicine
|October 10, 2018
PubMed
Summary

This study introduces a unified sample size planning method for the Wilcoxon-Mann-Whitney test, applicable to diverse data types including metric, count, and categorical data. It optimizes sample allocation for efficiency across various statistical scenarios.

Keywords:
Wilcoxon-Mann-Whitney testnonparametric relative effectnonparametric statisticsoptimal designrank-based inferencesample size planning

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Area of Science:

  • Biostatistics
  • Statistical Methods
  • Nonparametric Statistics

Background:

  • Existing sample size planning methods for the Wilcoxon-Mann-Whitney test are often limited to specific data types or statistical models.
  • A need exists for a flexible and unified approach to accommodate diverse data structures and improve the efficiency of sample size calculations.

Purpose of the Study:

  • To develop a unified sample size planning procedure for the Wilcoxon-Mann-Whitney test applicable to a wide range of data types.
  • To provide a method for calculating optimal sample size allocation that minimizes the total sample size required.
  • To characterize conditions under which a balanced sample size allocation is optimal.

Main Methods:

  • A 'synthetic data' approach is employed to estimate unknown theoretical quantities, such as variances under null and alternative hypotheses.
  • Empirical distribution functions are used to match theoretical distributions for calculating rank-based statistics.
  • The method computes the necessary sample size (N) for a fixed allocation proportion (t) and determines an optimal interval for t.

Main Results:

  • The unified approach successfully handles metric (with/without ties), count, ordered categorical, and dichotomous data.
  • An interval for the optimal allocation proportion (t) is provided, minimizing the total sample size.
  • The study identifies distributions where a balanced design (t=0.5) is optimal and shows that optimal allocation depends on variance ratios, differing from normal distribution models.

Conclusions:

  • The proposed unified method offers a versatile and efficient solution for sample size planning in the Wilcoxon-Mann-Whitney test across various data types.
  • Understanding the role of variance ratios in optimal sample allocation is crucial for maximizing statistical power and minimizing sample size.
  • The findings provide valuable guidance for researchers in designing studies using nonparametric tests.