ANOVA F-Statistic Calculator

Calculate the F-statistic for one-way ANOVA from between-group and within-group mean squares.

F-Statistic

4.000

df Between3
df Within36
Eta-Squared (Effect Size)0.2500

F-Statistic vs Mean Square Between Groups (MSB)

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Formula

## One-Way ANOVA F-Test ANOVA tests whether the means of two or more groups are significantly different by comparing between-group variance to within-group variance. ### Formula **F = MSB / MSW** where MSB = SSB/(k-1) is the mean square between groups and MSW = SSW/(N-k) is the mean square within groups. A large F indicates that group means differ more than expected by random chance.

Exemplo Resolvido

MSB = 120, MSW = 30, k = 4 groups, N = 40 total observations.

  1. 01F = 120 / 30 = 4.000
  2. 02df1 = 4 - 1 = 3, df2 = 40 - 4 = 36
  3. 03Critical F(3,36) at alpha=0.05 ≈ 2.87
  4. 04F = 4.0 > 2.87, so groups differ significantly