Kostenloser ANOVA F-Statistic Rechner
Berechnen Sie den F-statistic for one-way ANOVA aus mean squares. Test whether group means are significantly different.
F-Statistic
4.000
F-Statistic vs Mean Square Between Groups (MSB)
Formel
## 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.
Lösungsbeispiel
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
Häufig Gestellte Fragen
What assumptions does ANOVA require?
Independence of observations, normality within each group (checked with Shapiro-Wilk test), and homogeneity of variances (checked with Levene test). ANOVA is robust to mild violations with equal group sizes.
What do I do after a significant F-test?
A significant F-test says at least two means differ, but not which ones. Use post-hoc tests (Tukey HSD, Bonferroni, Scheffe) for pairwise comparisons while controlling family-wise error rate.
What is eta-squared?
Eta-squared (eta²) = SSB/SST is the proportion of total variance explained by group membership. It is the ANOVA analog of R². Cohen guidelines: 0.01 small, 0.06 medium, 0.14 large effect.
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