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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
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Randomized -values for multiple testing and their application in replicability analysis.

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  • 1Institute for Statistics, University of Bremen, Bremen, Germany.

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|January 19, 2021
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Summary
This summary is machine-generated.

Randomized p-values improve the estimation of true null hypotheses in replicability studies. This statistical method offers a more accurate assessment compared to traditional least favorable parameter configurations (LFCs).

Keywords:
Schweder-Spjøtvoll estimatorhazard ratio ordermeta-analysisproportion of true null hypotheses

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Area of Science:

  • Statistics
  • Genomics
  • Reproducibility Research

Background:

  • Simultaneous testing of multiple endpoints presents a multiple testing problem with composite null hypotheses.
  • Traditional p-values computed under least favorable parameter configurations (LFCs) are overly conservative for composite null hypotheses.
  • This conservatism complicates the estimation of the proportion of true null hypotheses, a key aspect of replicability analysis.

Purpose of the Study:

  • To investigate the application of randomized p-values for testing replicability hypotheses simultaneously across multiple endpoints.
  • To introduce a general class of statistical models enabling easy calculation of valid randomized p-values.
  • To compare the accuracy of randomized p-values against LFC-based approaches for estimating the proportion of true null hypotheses.

Main Methods:

  • Utilized randomized p-values as an alternative to traditional p-values in the context of multiple testing.
  • Developed a general class of statistical models amenable to randomized p-value computation.
  • Employed computer simulations to evaluate the performance of the proposed methodology.
  • Applied the methodology to a real-world genomics dataset.

Main Results:

  • Randomized p-values provide a more accurate estimation of the proportion of true null hypotheses compared to LFC-based methods.
  • The proposed statistical models facilitate straightforward calculation of valid randomized p-values.
  • Simulations confirmed the superior performance of randomized p-values in replicability analysis.

Conclusions:

  • Randomized p-values offer a valuable solution to the over-conservatism of traditional p-values in multiple testing scenarios with composite null hypotheses.
  • The proposed methodology enhances the accuracy of estimating the proportion of true null hypotheses in replicability studies.
  • The application to genomics data demonstrates the practical utility of randomized p-values in real-world scientific research.