Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies

A.O.J. Cramer, Don van Ravenzwaaij, Dora Matzke, Helen Steingroever, Ruud Wetzels, Raoul P P P Grasman, Lourens J Waldorp, Eric-Jan Wagenmakers

Research output: Contribution to journalArticleScientificpeer-review

292 Citations (Scopus)
41 Downloads (Pure)


Many psychologists do not realize that exploratory use of the popular multiway analysis of variance harbors a multiple-comparison problem. In the case of two factors, three separate null hypotheses are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14 % rather than 5 %, if the three tests are independent. We explain the multiple-comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus F test, control of the familywise error rate, control of the false discovery rate, and preregistration of the hypotheses.

Original languageEnglish
Pages (from-to)640-647
JournalPsychonomic Bulletin & Review
Issue number2
Publication statusPublished - 2016
Externally publishedYes


  • Analysis of Variance
  • Biomedical Research
  • Data Interpretation, Statistical
  • Humans
  • Psychology
  • Journal Article


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