One-Way ANOVA Calculator
Calculate the F-statistic, between/within group degrees of freedom, and eta-squared effect size for a one-way ANOVA across three groups.
Results
What is it?
One-way ANOVA tests whether the means of 3+ groups are equal by comparing between-group variance (signal) to within-group variance (noise). The F-statistic = MS_between / MS_within. A large F indicates the group means differ more than expected by chance. Use the F-distribution with (df_between, df_within) to find the p-value.
How to use
Enter sample size, mean, and standard deviation for each of the three groups. The calculator outputs F, degrees of freedom, and eta-squared. Look up the F critical value in an F-distribution table using df_between and df_within at your chosen alpha level.
Example scenario
Three teaching methods (n=10 each): Group 1 mean=50, Group 2 mean=55, Group 3 mean=60, all SD approx 8. Grand mean = 55. SS_between = 10x(25 + 0 + 25) = 500. SS_within = 9x(64+81+49) = 1746. MS_between = 250, MS_within = 64.7. F = 3.87, df=(2,27). Critical F(2,27) at p<0.05 = 3.35. F > 3.35, so reject H0 -- at least one group mean differs.
Pro tip
ANOVA critical F-values (alpha=0.05): F(2,27)=3.35, F(2,30)=3.32, F(2,60)=3.15. ANOVA assumptions: (1) normality within each group, (2) homogeneity of variance (Levene's test), (3) independence. If groups differ significantly, run post-hoc tests (Tukey HSD, Bonferroni) to find which specific pairs differ. Eta-squared: 0.01 = small, 0.06 = medium, 0.14 = large (Cohen, 1988). ANOVA with eta-sq < 0.06 may not be practically meaningful even if p < 0.05.