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To permute or not to permute.

Yifan Huang1, Haiyan Xu, Violeta Calian

  • 1H. Lee Moffitt Cancer Center & Research Institute, The University of South Florida Tampa, FL 33612, USA.

Bioinformatics (Oxford, England)
|July 28, 2006
PubMed
Summary

Permutation tests can inflate Type I errors when comparing means if distributions differ. These tests are best suited for detecting non-identical distributions, not just mean equality.

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Area of Science:

  • Statistics
  • Hypothesis Testing

Background:

  • Permutation tests are widely used for hypothesis testing when test statistic distributions are unknown.
  • They are often applied to compare means, using sample mean differences as test statistics.

Purpose of the Study:

  • To investigate the validity of permutation tests for equality of means when underlying distributions differ.
  • To identify limitations of permutation tests in scenarios with unequal variances, correlations, or skewness.

Main Methods:

  • Utilizing permutation tests with difference of sample means as the test statistic.
  • Simulating scenarios where two distributions are not identical but means are equal.

Main Results:

  • Permutation tests demonstrated an inflated Type I error rate under non-identical distributions, even with equal means.
  • This inflation occurs due to unequal variances, correlations, or skewness between the groups.

Conclusions:

  • Permutation tests for equality of means are unreliable when distributions are not identical.
  • The application of permutation testing should be restricted to detecting non-identical distributions rather than solely mean equality.

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