The Fallacy of Placing Confidence in Confidence Intervals
by Richard D. Morey, Rink Hoekstra, Jeffrey N. Rouder, Michael D. Lee, Eric-Jan Wagenmakers · Psychonomic Bulletin & Review
Uses a submersible-rescue thought experiment to construct four valid 50% intervals for the same problem, showing that coverage alone guarantees neither precision nor plausibility, and naming the fundamental confidence, precision, and likelihood fallacies. The lifeboat example is concrete enough to follow without measure theory, yet it demolishes the intuition that a narrower interval means a more precise estimate.
More resources on Confidence Intervals
stattrek.com
StatTrek is an online statistics resource that provides clear tutorials and explanations of probability and statistics. It also features free calculators for distributions, hypothesis tests, confidence intervals, and other statistical methods.
Statistical Intervals: A Guide for Practitioners and Researchers (2nd Edition)
A 592-page reference separating confidence, prediction, and tolerance intervals, covering which one a given question actually calls for, distribution-free methods, likelihood-based intervals, bootstrap and simulation approaches, and sample-size planning for a target interval width.
Introduction to Probability and Statistics: Lecture Notes (MIT 18.05)
Slide-based class notes for the course; classes 22 to 24 build confidence intervals for normal data, relate pivots, hypothesis-test inversion and coverage, and derive bootstrap intervals. Paired with solved problem sets and exams, they teach learners to construct and interpret intervals.
Interpreting Confidence Intervals — Interactive Visualization
A D3 simulation that draws repeated samples and plots each resulting interval against the true mean, with adjustable sample size and confidence level, plus the sampling distribution of interval width to show that precision itself varies.
Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations
Seven senior statisticians and epidemiologists enumerate 25 common misinterpretations of p-values, confidence intervals, and power, correcting each one and reframing intervals as compatibility ranges rather than probability statements about parameters. The single most-cited corrective on what a confidence interval actually claims. Items 19-24 deal specifically with intervals: the interval is not a 95% probability region for the parameter, values outside it are not refuted, and values inside are not equally supported. It teaches the inference mental model rather than the arithmetic.
statisticshowto.com
Statistics How To is a practical statistics learning site that explains core concepts with clear, step-by-step tutorials and worked examples. It covers hypothesis testing (including p-values and test types) along with a wide range of other stats topics and handy calculators.