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Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ

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  • J. van Doorn
  • A. Ly
  • M. Marsman
  • E.-J. Wagenmakers

Abstract

Bayesian inference for rank-order problems is frustrated by the absence of an explicit likelihood function. This hurdle can be overcome by assuming a latent normal representation that is consistent with the ordinal information in the data: the observed ranks are conceptualized as an impoverished reflection of an underlying continuous scale, and inference concerns the parameters that govern the latent representation. We apply this generic data-augmentation method to obtain Bayes factors for three popular rank-based tests: the rank sum test, the signed rank test, and Spearman's $\rho _s $ρs.

Suggested Citation

  • J. van Doorn & A. Ly & M. Marsman & E.-J. Wagenmakers, 2020. "Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(16), pages 2984-3006, December.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:16:p:2984-3006
    DOI: 10.1080/02664763.2019.1709053
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    Cited by:

    1. Riko Kelter, 2021. "Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality," Computational Statistics, Springer, vol. 36(2), pages 1263-1288, June.
    2. Kelter, Riko, 2022. "Power analysis and type I and type II error rates of Bayesian nonparametric two-sample tests for location-shifts based on the Bayes factor under Cauchy priors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    3. Suzanne Hoogeveen & Julia M. Haaf & Joseph A. Bulbulia & Robert M. Ross & Ryan McKay & Sacha Altay & Theiss Bendixen & Renatas Berniūnas & Arik Cheshin & Claudio Gentili & Raluca Georgescu & Will M. G, 2022. "The Einstein effect provides global evidence for scientific source credibility effects and the influence of religiosity," Nature Human Behaviour, Nature, vol. 6(4), pages 523-535, April.

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