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Significance test for linear regression: how to test without P-values?

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Summary

This study re-examines p-value accuracy, finding it unreliable in some cases. Alternative methods like Minimum Bayes Factors offer more reliable hypothesis testing, especially when the null hypothesis is false.

Keywords:
Ban of P-valueMinimum Bayes Factorsbelief functions

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Area of Science:

  • Statistics
  • Econometrics
  • Scientific Research Methodology

Background:

  • The 2016 American Statistician Association discussion highlighted the misuse of p-values in scientific research.
  • Researchers, particularly economists, may misinterpret guidelines on significance testing and p-value usage.
  • There is a need to re-evaluate the reliability of p-values and explore alternative hypothesis testing methods.

Purpose of the Study:

  • To re-examine the accuracy and reliability of p-values in statistical inference.
  • To introduce and evaluate alternative methods for hypothesis testing, including Minimum Bayes Factors and Belief functions.
  • To compare the performance of p-values with alternative approaches under different conditions.

Main Methods:

  • A simulation study was conducted to investigate the reliability of p-values.
  • Existing approaches, Minimum Bayes Factors (MBFs) and Belief functions, were introduced as potential replacements for p-values.
  • The accuracy of a plausibility approach was compared against traditional p-values for decisions about the null hypothesis.

Main Results:

  • Simulation results confirmed that p-values can be unreliable in certain scenarios.
  • The proposed alternative approaches demonstrated utility as substitutes for p-values in statistical inference.
  • The plausibility approach showed higher accuracy than p-values when the null hypothesis was true.
  • Minimum Bayes Factors (MBFs) provided more reliable results than other methods when the null hypothesis was false.

Conclusions:

  • P-values exhibit limitations in reliability, necessitating the exploration of alternative statistical tools.
  • Minimum Bayes Factors and Belief functions show promise as more dependable methods for hypothesis testing.
  • The study advocates for the adoption of more robust statistical approaches to enhance the validity of scientific conclusions.