Lesson 1: Introduction to ANOVA

Analysis of Variance (ANOVA)

Suppose we want to compare the effectiveness of 3 different diets (A, B, and C).

If we used t-tests, we’d have to compare A vs B, B vs C, and A vs C. This increases the chance of a Type I error (finding a difference when there isn’t one).

The F-Statistic

ANOVA compares the variance between the groups to the variance within the groups.

$F = \frac{\text{Variance Between Groups}}{\text{Variance Within Groups}}$

Interpreting F

Large F

The groups are very different from each other compared to the noise within them.

Result

Reject $H_0$ . At least one group mean is different.

Small F

The differences between groups are likely just random noise.

Result

Fail to Reject $H_0$ . No significant difference.

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Lesson 1