One-way ANOVA
Analysis of variance (ANOVA) compares the means of three or more groups at once. It checks whether the variation between group means is large compared with the variation inside the groups.
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Analogy
If classes' averages differ more than students within a class differ, the classes probably are not the same.
Example
A: 4, 5, 6 (mean 5)B: 6, 7, 8 (mean 7)C: 8, 9, 10 (mean 9)Grand mean = 7Between SS = 3 x (4 + 0 + 4) = 24Within SS = 2 + 2 + 2 = 6
In practice
Compares crop yields from three fertilisers or reaction times under three conditions.
Practice
Flashcards
- What does ANOVA test?Whether three or more group means are all equal.
Interview questions
- Why use ANOVA instead of several t tests, and what does the F statistic compare?
- Many t tests inflate the false alarm rate
- ANOVA tests all means at once
- F compares between-group and within-group variation
- A large F suggests real differences
- A post-hoc test finds which groups differ
Questions people ask
Why not just run several t tests instead of ANOVA?
Each t test carries a 5 percent false alarm chance, and the chances add up. Three pairwise tests give about a 14 percent chance of at least one false alarm. ANOVA tests all the means with one overall test and keeps the error rate at 5 percent.
What are the null and alternative hypotheses in ANOVA?
The null says all group means are equal. The alternative says at least one mean is different. A significant result does not say which groups differ. A follow-up comparison is needed to find that out, since the overall test only raises a flag that something differs.