--- title: Confidence Intervals description: Confidence intervals provide an estimated range of values likely to contain an unknown population parameter. Learners will understand how to calculate and interpret these intervals to quantify the uncertainty and precision of statistical estimates. category: mathematics subcategory: probability-theory difficulty: beginner, intermediate, advanced url: /subject/statistics-and-probability-confidence-intervals --- # Confidence Intervals Confidence intervals provide an estimated range of values likely to contain an unknown population parameter. Learners will understand how to calculate and interpret these intervals to quantify the uncertainty and precision of statistical estimates. ## Available Resources 2 Books • 3 Courses • 3 Websites • 2 Papers ## Books ### 1. Statistical Intervals: A Guide for Practitioners and Researchers (2nd Edition) **Author:** William Q. Meeker, Gerald J. Hahn, Luis A. Escobar 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. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0471687170?tag=edmonddante07-20 **Tags:** confidence-intervals, prediction-intervals, tolerance-intervals, bootstrap, sample-size ### 2. Statistics Done Wrong **Author:** Alex Reinhart Alex Reinhart's short survey of the statistical errors common in published science, including misread p-values, underpowered studies, pseudoreplication, multiple comparisons, and regression to the mean, so readers can spot flawed analyses and avoid repeating them in their own research. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1593276206?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, statistics-and-probability ## Courses ### 1. Introduction to Probability and Statistics: Lecture Notes (MIT 18.05) **Author:** Jeremy Orloff, Jennifer French Kamrin 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/lecture-notes/ **Tags:** confidence-intervals, bootstrap, hypothesis-testing, statistical-inference, probability ### 2. Statistics with R University of Colorado Boulder course, taught by Charlie Nuttelman, that uses R and RStudio for applied statistics. Covers descriptive statistics, probability distributions, confidence intervals, one- and two-sample hypothesis tests, regression and ANOVA, so learners can run and interpret standard analyses in R. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/statistics-and-data-analysis-with-r **Tags:** courses, science-research, scientific-method ### 3. Introduction to Statistics Stanford's "Introduction to Statistics" teaches you statistical thinking concepts that are essential for learning from data and communicating insights. By the end of the course, you will be able to perform exploratory data analysis, understand key principles of sampling, and select appropriate tests of significance for multiple contexts. You will gain the foundational skills that prepare you to pursue more advanced topics in statistical thinking and machine learning. Topics include Descriptive Statistics, Sampling and Randomized Controlled Experiments, Probability, Sampling Distributions and the Central Limit Theorem, Regression, Common Tests of Significance, Resampling, Multiple Comparisons. **Difficulty:** Beginner | **Language:** English | **Duration:** This course will take approx. 6-8 hours to complete, depending on prior knowledge and experience. | **Price:** Free **Link:** https://www.coursera.org/learn/stanford-statistics **Tags:** courses, mathematics-statistics, statistics-and-probability ## Websites ### 1. Interpreting Confidence Intervals — Interactive Visualization **Author:** Kristoffer Magnusson 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. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://rpsychologist.com/d3/ci/ **Tags:** confidence-intervals, simulation, sampling-distribution, coverage, interactive-visualization ### 2. 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://statisticshowto.com **Tags:** websites, mathematics-statistics, statistics-and-probability ### 3. 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://stattrek.com **Tags:** websites, science-research, scientific-method ## Papers ### 1. The Fallacy of Placing Confidence in Confidence Intervals **Author:** Richard D. Morey, Rink Hoekstra, Jeffrey N. Rouder, Michael D. Lee, Eric-Jan Wagenmakers 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. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://pmc.ncbi.nlm.nih.gov/articles/PMC4742505/ **Tags:** confidence-intervals, frequentist-inference, bayesian-statistics, credible-intervals, statistical-fallacies ### 2. Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations **Author:** Sander Greenland, Stephen J. Senn, Kenneth J. Rothman, John B. Carlin, Charles Poole, Steven N. Goodman, Douglas G. Altman 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://pmc.ncbi.nlm.nih.gov/articles/PMC4877414/ **Tags:** p-values, confidence-intervals, statistical-power, hypothesis-testing, statistical-misinterpretation --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. 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