The fallacy of placing confidence in confidence intervals

Richard D. Morey, Rink Hoekstra, Jeffrey N. Rouder, Michael D. Lee, Eric-Jan Wagenmakers

Research output: Contribution to journalArticleAcademicpeer-review

283 Citations (Scopus)
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Abstract

Interval estimates – estimates of parameters that include an allowance for sampling uncertainty – have long been touted as a key component of statistical analyses. There are several kinds of interval estimates, but the most popular are confidence intervals (CIs): intervals that contain the true parameter value in some known proportion of repeated samples, on average. The width of confidence intervals is thought to index the precision of an estimate; CIs are thought to be a guide to which parameter values are plausible or reasonable; and the confidence coefficient of the interval (e.g., 95 %) is thought to index the plausibility that the true parameter is included in the interval. We show in a number of examples that CIs do not necessarily have any of these properties, and can lead to unjustified or arbitrary inferences. For this reason, we caution against relying upon confidence interval theory to justify interval estimates, and suggest that other theories of interval estimation should be used instead.
Original languageEnglish
Pages (from-to)103-123
Number of pages21
JournalPsychonomic Bulletin and Review
Volume23
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • EFFECT SIZE
  • P-VALUES
  • STATISTICAL-INFERENCE
  • FIDUCIAL ARGUMENT
  • ANOVA DESIGNS
  • HYPOTHESIS
  • PROBABILITY
  • OBJECTIONS
  • INDUCTION
  • STUDENTS

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