Free 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)
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.
Example Calculation
MSB = 120, MSW = 30, k = 4 groups, N = 40 total observations.
- 01F = 120 / 30 = 4.000
- 02df1 = 4 - 1 = 3, df2 = 40 - 4 = 36
- 03Critical F(3,36) at alpha=0.05 ≈ 2.87
- 04F = 4.0 > 2.87, so groups differ significantly
Frequently Asked Questions
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