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Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses.

M J Bayarri1, Daniel J Benjamin2, James O Berger3

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This study proposes using the odds of correct versus incorrect hypothesis rejections as a superior alternative to p-values. This method offers a more robust statistical inference, enhancing scientific rigor in hypothesis testing.

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Bayes factorsBayesianFrequentistOdds

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Area of Science:

  • Statistics
  • Scientific Methodology
  • Hypothesis Testing

Background:

  • Hypothesis testing is central to scientific research.
  • Sole reliance on p-values for inference is a long-standing issue.
  • Current practices face significant criticism for statistical limitations.

Purpose of the Study:

  • To introduce an alternative to p-value-based inference in hypothesis testing.
  • To propose using the odds of correct to incorrect null hypothesis rejection.
  • To provide practical implementations for this new statistical approach.

Main Methods:

  • Development of pre-experimental (power, Type I error) and post-experimental (data-dependent) measures.
  • Implementation strategies ranging from p-value-only to full Bayesian analysis.
  • Ensuring all methods maintain a frequentist justification.

Main Results:

  • The proposed odds-based method offers a more informative alternative to p-values.
  • Implementations are flexible, accommodating various levels of analytical complexity.
  • All proposed methods, including Bayesian approaches, are grounded in frequentist principles.

Conclusions:

  • The odds of correct to incorrect rejection provide a statistically sound alternative to p-values.
  • This approach can be integrated with minor modifications to existing practices.
  • The proposed method addresses critical shortcomings in current hypothesis testing paradigms.