--- title: Inferential Statistics description: Inferential statistics involves using data from a sample to make generalizations about a larger population. You will understand how to perform hypothesis testing, calculate confidence intervals, and estimate population parameters while accounting for sampling error. category: programming-tech subcategory: data-science difficulty: beginner, intermediate, advanced url: /subject/inferential-statistics --- # Inferential Statistics Inferential statistics involves using data from a sample to make generalizations about a larger population. You will understand how to perform hypothesis testing, calculate confidence intervals, and estimate population parameters while accounting for sampling error. ## Available Resources 1 Videos • 3 Books • 3 Courses • 7 Websites ## Websites ### 1. OpenIntro Statistics Free open-source introductory statistics textbook, with chapters on sampling distributions, confidence intervals, hypothesis tests, and regression. Worked examples, real datasets, exercise solutions and lab material let readers practise inference rather than only read about it. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.openintro.org/book/stat/ **Tags:** statistics, hypothesis-testing, confidence-intervals, textbook, open-access ### 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 ### 4. inferentialthinking.com Inferential Thinking is a learning resource that introduces inferential statistics with clear explanations, visuals, and practical examples. It offers tutorials, articles, and practice problems covering sampling, probability, confidence intervals, hypothesis testing, and data analysis techniques. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://inferentialthinking.com **Tags:** websites, technology-computer-science, data-science--ai ### 5. seeing-theory.brown.edu Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://seeing-theory.brown.edu **Tags:** websites, technology-computer-science, data-science--ai ### 6. effectsizefaq.com EffectSizeFAQ.com is a concise FAQ-style resource that explains effect sizes used in inferential statistics. It covers common measures (Cohen's d, Pearson's r, odds ratios), how to compute and interpret them, and how to report results with practical examples. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://effectsizefaq.com **Tags:** websites, technology-computer-science, statistics-data-science ### 7. stats.stackexchange.com Stats Stack Exchange is a Q&A community for statistics professionals and enthusiasts, featuring questions and expert answers on topics from probability and inference to data analysis and experimental design. It’s a practical resource for learning statistical concepts, getting help with methods, and discussing real-world data problems. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://stats.stackexchange.com **Tags:** websites, technology-computer-science, data-science--ai ## Videos ### 1. StatQuest: Hypothesis Testing and P-values Josh Starmer's StatQuest walkthrough of what a null hypothesis is, how a test statistic is compared against it, and how p-values are interpreted. Uses drawn examples and plain language instead of formal derivations. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=0oc49DyA3hU **Tags:** hypothesis-testing, p-values, null-hypothesis, statistics, video-explainer ## Courses ### 1. Statistics Learn statistics fundamentals with this free course from Khan Academy! Master probability, data analysis, and more. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/statistics-probability **Tags:** introductory-statistics, probability, data-analysis, hypothesis-testing ### 2. Inferential Stats Inferential statistics are concerned with making inferences based on relations found in the sample, to relations in the population. Inferential statistics help us decide, for example, whether the differences between groups that we see in our data are strong enough to provide support for our hypothesis that group differences exist in general, in the entire population. We will start by considering the basic principles of significance testing: the sampling and test statistic distribution, p-value, significance level, power and type I and type II errors. Then we will consider a large number of statistical tests and techniques that help us make inferences for different types of data and different types of research designs. For each individual statistical test we will consider how it works, for what data and design it is appropriate and how results should be interpreted. Normally you would also learn how to perform these tests using freely available software R. Due to technical issues we are not able to do so. We will try to offer this again soon. For those who are already familiar with statistical testing: We will look at z-tests for 1 and 2 proportions, McNemar's test for dependent proportions, t-tests for 1 mean (paired differences) and 2 means, the Chi-square test for independence, Fisher’s exact test, simple regression (linear and exponential) and multiple regression (linear and logistic), one way and factorial analysis of variance, and non-parametric tests (Wilcoxon, Kruskal-Wallis, sign test, signed-rank test, runs test). **Difficulty:** Beginner | **Language:** English | **Duration:** 7 weeks of study, 1-3 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/inferential-statistics **Tags:** courses, technology-computer-science, data-science--ai ### 3. Introduction to Probability **Author:** Joe Blitzstein HarvardX's self-paced version of Harvard's Stat 110, taught by Joe Blitzstein. Covers counting and story proofs, conditional probability and Bayes' rule, discrete and continuous random variables, joint distributions, the law of large numbers, the central limit theorem and Markov chains. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/probability/harvard-university-introduction-to-probability **Tags:** probability, random-variables, bayes-rule, probability-distributions, markov-chains, central-limit-theorem ## Books ### 1. Practical Statistics for Data Scientists **Author:** Peter Bruce, Andrew Bruce A concise statistics book written for programmers that covers sampling, experimental design, A/B testing, regression, classification, and resampling, with R code throughout. Readers learn which statistical ideas matter for data science and how sampling and study design shape the conclusions data can support. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1491952962?tag=edmonddante07-20 **Tags:** applied-statistics, data-science, ab-testing, regression, resampling, r-programming ### 2. All of Statistics **Author:** Larry Wasserman Fast-moving graduate survey covering probability, estimation, hypothesis testing, bootstrap, Bayesian inference and basic statistical models in one volume. Written for computer scientists who need the inferential toolkit quickly, it assumes calculus and skips lengthy derivations. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1441923225?tag=edmonddante07-20 **Tags:** books, technology-computer-science, data-science--ai ### 3. Statistical Inference **Author:** George Casella and Roger L. Berger Standard first-year graduate text in mathematical statistics. Develops probability, transformations, sampling distributions, point estimation, hypothesis testing and interval estimation with full proofs, giving readers the theoretical grounding assumed by PhD-level statistics and econometrics courses. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/7111109457?tag=edmonddante07-20 **Tags:** books, technology-computer-science, data-science--ai --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/inferential-statistics