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The Bayesian highest-density interval plus region of practical equivalence (HDI + ROPE) procedure for null hypothesis testing is logically flawed. Its reliance on probability density, not probability, makes decisions arbitrary and scientifically irrelevant.

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Psychological Science

Background:

  • The Bayesian highest-density interval plus region of practical equivalence (HDI + ROPE) is a common method for null hypothesis testing.
  • This procedure compares a posterior highest-density interval (HDI) with a region of practical equivalence (ROPE).

Purpose of the Study:

  • To demonstrate the logical incoherence of the HDI + ROPE decision rule.
  • To identify the theoretical underpinnings of this incoherence and propose alternatives.

Main Methods:

  • Theoretical analysis of the HDI + ROPE procedure.
  • Examination of statistical model properties, including transformation invariance.
  • Distinguishing between probability density and probability proper.

Main Results:

  • The HDI + ROPE procedure is logically incoherent.
  • The HDI's lack of transformation invariance leads to decisions based on arbitrary statistical properties.
  • The procedure confuses probability density with probability proper.

Conclusions:

  • The HDI + ROPE procedure is statistically flawed and should be avoided.
  • Alternative Bayesian testing procedures, such as quantile intervals, are recommended.
  • Researchers should use methods that are based on probability, not just density.