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On generalized Simes critical constants.

Jiangtao Gou1, Ajit C Tamhane

  • 1Department of Statistics, Northwestern University, 2006 Sheridan Road, Evanston, IL, 60208, USA.

Biometrical Journal. Biometrische Zeitschrift
|September 19, 2014
PubMed
Summary
This summary is machine-generated.

This study enhances the Simes test for multiple hypothesis testing by introducing higher-order critical constants. Third-order constants show improved power, but practical use is limited for orders greater than three.

Keywords:
Multiple hypothesesPowerSimes testType I error

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Area of Science:

  • Statistics
  • Hypothesis Testing
  • Biostatistics

Background:

  • The Simes test is a widely used method for testing the overall null hypothesis in multiple hypothesis testing scenarios.
  • Existing Cai-Sarkar generalized Simes critical constants offer improved power over the original Simes test, particularly when multiple null hypotheses are false.

Purpose of the Study:

  • To extend the computation of Simes critical constants to third order and arbitrary kth order.
  • To evaluate the power of these higher-order constants in improving the Simes test's performance.

Main Methods:

  • Development of a method to compute third-order and arbitrary kth-order Simes critical constants, extending the Cai-Sarkar approach.
  • Utilized simulation studies to compare the power of the proposed higher-order constants against existing methods.

Main Results:

  • Third-order Simes constants demonstrate superior power compared to second-order Cai-Sarkar constants in most tested scenarios for overall null hypothesis testing.
  • The study provides a framework for extending Simes constants to arbitrary kth order.

Conclusions:

  • Higher-order Simes constants, particularly third-order, offer a statistically significant improvement in testing power.
  • Practical application of constants for k>3 is limited due to associated drawbacks, suggesting a trade-off between power and complexity.