ANOVA Variance Ratio (F-Test) – AP Statistics

Analysis of Variance (ANOVA)

Tests if 3 or more population means are equal by comparing two sources of variability.

The F-Ratio Statistic

$$ F = \frac{\text{MSB}}{\text{MSW}} $$

MSB (Between-Group Spread): How far the group means (colored lines) are from the global mean (dashed line).

MSW (Within-Group Spread): How scattered the raw points are around their own group mean.

Hypotheses

$H_0$: $\mu_1 = \mu_2 = \mu_3$

$H_A$: At least one mean is different.