--- title: ANOVA description: Analysis of Variance (ANOVA) is a statistical method used to compare means across three or more groups. Learners will understand how to partition variance, perform one-way and two-way ANOVA tests, and interpret post-hoc analyses. category: mathematics subcategory: probability-theory difficulty: beginner, intermediate, advanced url: /subject/statistics-and-probability-anova --- # ANOVA Analysis of Variance (ANOVA) is a statistical method used to compare means across three or more groups. Learners will understand how to partition variance, perform one-way and two-way ANOVA tests, and interpret post-hoc analyses. ## Available Resources 2 Books • 2 Courses • 4 Websites • 1 Papers ## Books ### 1. Design and Analysis of Experiments (10th Edition) **Author:** Douglas C. Montgomery The standard graduate text on designed experiments: single-factor ANOVA, model adequacy checking, randomized blocks, Latin squares, factorial and fractional factorial designs, random and mixed models, and response surfaces, with real data sets and software output throughout. It is the reference where ANOVA lives inside its proper home — experimental design — and no free resource matches its depth on model adequacy checking, mixed models and fractional factorials. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1119492491?tag=edmonddante07-20 **Tags:** anova, design-of-experiments, factorial-designs, mixed-models, response-surface ### 2. Learning Statistics with R **Author:** Danielle Navarro A free CC-licensed textbook whose one-way and factorial ANOVA chapters derive the F test from sums-of-squares partitioning, then cover effect sizes, assumption checks, post-hoc corrections, Type I/II/III sums of squares, and the equivalence with linear regression. Chapter 14 (one-way ANOVA) and Chapter 16 (factorial ANOVA) explain why variance is partitioned and where assumptions break, including the Type I/II/III sums-of-squares trap that most intro material ignores. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://learningstatisticswithr.com/ **Tags:** statistics, r, anova, linear-regression, hypothesis-testing ## Websites ### 1. R Library: Contrast Coding Systems for Categorical Variables UCLA's statistical consulting reference works through dummy, simple, deviation, Helmert, reverse Helmert, polynomial and difference coding schemes, showing with R output how each changes what the coefficients and planned comparisons in a factor model actually estimate. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://stats.oarc.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/ **Tags:** contrast-coding, categorical-variables, r, regression, anova ### 2. Common statistical tests are linear models (or: how to teach stats) **Author:** Jonas Kristoffer Lindeløv A worked demonstration that t-tests, one-way and two-way ANOVA, ANCOVA and their rank-based counterparts are all special cases of the linear model, with R code, side-by-side output and a printable cheat sheet mapping each test to its regression form. It kills the idea that ANOVA is a separate procedure by showing the identical parameter estimates from lm(). Community consensus has effectively made it the standard reference, **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://lindeloev.github.io/tests-as-linear/ **Tags:** linear-models, anova, t-test, nonparametric-tests, r ### 3. 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 ### 4. 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. Analysis of Variance: Why It Is More Important Than Ever **Author:** Andrew Gelman Gelman's Annals of Statistics paper recasts ANOVA as a multilevel model in which each table row is a batch of exchangeable effects, arguing this handles unbalanced and split-plot designs correctly and shifts the focus from significance tests to variance-component estimates. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://arxiv.org/abs/math/0504499 **Tags:** anova, multilevel-models, variance-components, bayesian-statistics ## Courses ### 1. STAT 502: Analysis of Variance and Design of Experiments Penn State's graduate course notes on analysis of variance and experimental design, covering ANOVA foundations, multiple comparisons, blocking, random and mixed effects, factorial and split-plot designs, with worked examples and software output. The most complete free treatment of the topic: it builds variance partitioning from first principles, then extends to blocking, random/mixed effects and split-plot designs rather than stopping at one-way F tests. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://online.stat.psu.edu/stat502/ **Tags:** anova, design-of-experiments, multiple-comparisons, mixed-models, split-plot-designs ### 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 --- *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/statistics-and-probability-anova