ANOVA F-Ratio Calculator
Calculate the ANOVA F-ratio from between-group and within-group mean squares to test whether group means differ significantly.
F-Ratio
4.0000
F-Ratio vs Mean Square Between (MSB)
Formula
## 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.
Exemplo Resolvido
Three groups, 30 total observations. MSB = 120, MSW = 30.
- 01F = MSB / MSW = 120 / 30 = 4.0
- 02df between = 3 - 1 = 2
- 03df within = 30 - 3 = 27
- 04Eta-squared = (120*2) / (120*2 + 30*27) = 240 / 1050 = 0.2286
- 05About 22.9% of total variance is explained by group membership
Perguntas Frequentes
What does a significant F-ratio tell me?
It tells you that at least one group mean is significantly different from the others, but not which groups differ. Post-hoc tests (Tukey, Bonferroni) are needed to identify specific pairwise differences.
What are the assumptions of ANOVA?
Observations are independent, each group is approximately normally distributed, and variances are roughly equal across groups (homogeneity of variance). ANOVA is fairly robust to moderate violations.
What is eta-squared?
Eta-squared is the proportion of total variance explained by the grouping variable. It is the ANOVA analog of R-squared. Values of 0.01, 0.06, and 0.14 correspond roughly to small, medium, and large effects.
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