ANOVA F-Ratio Calculator — 公式

## How to Calculate the ANOVA F-Ratio

### Formula

**F = MSB / MSW**

ANOVA (Analysis of Variance) tests whether the means of three or more groups are equal. MSB (Mean Square Between) measures variability between group means. MSW (Mean Square Within) measures variability within groups. A large F-ratio means between-group differences are large relative to within-group noise.

计算示例

Three groups, 30 total observations. MSB = 120, MSW = 30.

  1. F = MSB / MSW = 120 / 30 = 4.0
  2. df between = 3 - 1 = 2
  3. df within = 30 - 3 = 27
  4. Eta-squared = (120*2) / (120*2 + 30*27) = 240 / 1050 = 0.2286
  5. About 22.9% of total variance is explained by group membership