The fallacy of placing confidence in confidence intervals

Today we’ve discussed the following paper about the reliability of confidence intervals:

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

Psychonomic Bulletin & Review. Volume 23, pages 103–123 (2016).

Theoretical Review. Open Access. Published: 08 October 2015

Morey and colleagues define interval estimates and confidence intervals as follows:

• Interval estimates are a key component of statistical analysis and there are several kinds of interval estimates although the most popular are confidence intervals (CIs).
• Confidence intervals (CIs) are intervals that contain the true parameter value in some known proportion of repeated samples, on average, ans satisfy the following properties:
  • The width of CIs is thought to index the precision of an estimate
  • CIs are thought to be a guide to which parameter values are reasonable.
  • The confidence coefficient of the interval (e.g., 95%) is thought to index the plausibility that the true parameter is included in the interval.

What the authors showed in this paper is a number of examples in which CIs do not necessarily have any of these properties, and can lead to unjustified or arbitrary inferences. For this reason, they caution against relying upon confidence interval theory to justify interval estimates, and suggest that other theories of interval estimation should be used instead.

Sources

Feature image from Pexels – C0 license.