ANOVA in R

Learn how to perform an Analysis Of VAriance (ANOVA) in R to compare 3 groups or more. See also how to interpret the results and perform post-hoc tests

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Introduction

ANOVA (ANalysis Of VAriance) is a statistical test to determine whether two or more population means are different. In other words, it is used to compare two or more groups to see if they are significantly different.

In practice, however, the:

• Student t-test is used to compare 2 groups;
• ANOVA generalizes the t-test beyond 2 groups, so it is used to compare 3 or more groups.

Note that there are several versions of the ANOVA (e.g., one-way ANOVA, two-way ANOVA, mixed ANOVA, repeated measures ANOVA, etc.). In this article, we present the simplest form only — the one-way ANOVA1 — and we refer to it as ANOVA in the remaining of the article.

Although ANOVA is used to make inference about means of different groups, the method is called “analysis of variance”. It is called this because it compares the “between” variance (the variance between the different groups) and the variance “within” (the variance within each group). If the between variance is significantly larger than the within variance, the group means…