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A power fallacy.

Eric-Jan Wagenmakers1, Josine Verhagen2, Alexander Ly2

  • 1Department of Psychology, University of Amsterdam, Weesperplein 4, 1018 XA, Amsterdam, The Netherlands. ej.wagenmakers@gmail.com.

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Summary
This summary is machine-generated.

The power fallacy wrongly assumes high-power experiments are always more informative. This study shows low-power experiments can yield crucial insights, unlike high-power ones, challenging traditional statistical inference.

Keywords:
Bayes factorHypothesis testLikelihood ratioStatistical evidence

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Area of Science:

  • Statistics
  • Scientific Methodology

Background:

  • The power fallacy is a common misconception in statistical inference.
  • It incorrectly assumes that high-power experiments consistently provide more informative results than low-power experiments.

Purpose of the Study:

  • To expose the power fallacy with concrete examples.
  • To demonstrate that experimental outcomes, not just power, determine informativeness.
  • To recommend alternative inference methods for observed data.

Main Methods:

  • Illustrative examples of high- and low-power experiments.
  • Comparison of inference from observed data versus hypothetical replications.
  • Introduction of likelihood ratios and Bayes factors for data-driven inference.

Main Results:

  • High-power experiment outcomes can be uninformative.
  • Low-power experiment outcomes can be highly informative.
  • Power is less useful and potentially misleading for inferring from observed data.

Conclusions:

  • The power fallacy is a critical misconception in scientific reasoning.
  • Likelihood ratios and Bayes factors offer a more rational approach to quantify evidence from observed data.
  • These methods condition on actual data, avoiding misleading averages over hypothetical experiments.