On Mixture Alternatives and Wilcoxon’s Signed-Rank Test

J.D. Rosenblatt, Y. Benjamini

Research output: Contribution to journalArticlepeer-review


The shift alternative model has been the canonical alternative hypothesis since the early days of statistics. This holds true both in parametric and nonparametric statistical testing. In this contribution, we argue that in several applications of interest, the shift alternative is dubious while a mixture alternative is more plausible, because the treatment is expected to affect only a subpopulation. When considering mixture hypotheses, classical tests may no longer enjoy their desirable properties. In particular, we show that the t-test may be underpowered compared to Wilcoxon’s signed-rank test, even under a Gaussian null. We consider implications to personalized medicine and medical imaging. © 2018, © 2018 American Statistical Association.
Original languageEnglish
Pages (from-to)344-347
Number of pages4
JournalAmerican Statistician
Issue number4
StatePublished - 2018


FundersFunder number
Seventh Framework Programme294519
European Research Council
Israel Science Foundation900/16
Seventh Framework Programme


    • Efficiency
    • Hypothesis testing
    • Mixture model


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