Statistics Calculators

F-Statistic Calculator (One-Way ANOVA)

Calculate the F-statistic for a one-way ANOVA comparing three groups, from each group's mean, sample variance and size.

F-statistic —

Mean square between (MSB) —

Mean square within (MSW) —

df between —

df within —

About the F-Statistic Calculator (One-Way ANOVA)

One-way ANOVA tests whether the means of three or more groups differ significantly by comparing the variance between group means to the variance within each group. This calculator handles the common three-group case from each group's summary statistics.

Formula: MSB = ∑ nᵢ(x̄ᵢ − grand mean)² ÷ (k − 1) · MSW = ∑(nᵢ − 1)sᵢ² ÷ (N − k) · F = MSB ÷ MSW

A large F-statistic indicates the between-group variation greatly exceeds the within-group variation, suggesting at least one group mean differs from the others — compare it against an F critical value to test significance.