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📚 Mostly Harmless Statistics
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1 Introduction to Data2 Organizing Data3 Descriptive Statistics4 Probability5 Discrete Probability Distributions6 Continuous Probability Distributions7 Confidence Intervals for One Population8 Hypothesis Tests for One Population9 Hypothesis Tests and Confidence Intervals for Two Populations10 Chi-Square Tests11 Analysis of Variance12 Correlation and Regression13 Nonparametric Tests

Chapter 11: Analysis of Variance

The z- and t-tests can be used to test the equality between two population means μ1 and μ2. When we have more than two groups, we would inflate the probability of making a type I error if we were to compare just two at a time and make a conclusion about all the groups together. To account for this P(Type I Error) inflation, we instead will do an analysis of variance (ANOVA) to test the equality between 3 or more population means μ1,μ2,μ3,…,μk.

The F-test (for ANOVA) is a statistical test for testing the equality of k population means.

The one-way ANOVA F-test is a statistical test for testing the equality of k population means from 3 or more groups within one variable or factor. There are many different types of ANOVA; for now, we are going to start with what is commonly referred to as a one-way ANOVA, which has one main effect or factor that is split up into three or more independent treatment levels. In more advanced courses you would learn about dependent groups or two or more factors.

Assumptions:

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University), hosted on LibreTexts (stats.libretexts.org) and licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.