One-Way ANOVA Calculator
Run a one-way ANOVA on three groups and get the F statistic and p-value.
Input Data
Mean of group 1.
SD of group 1 (>0).
Size of group 1.
Mean of group 2.
SD of group 2 (>0).
Size of group 2.
Mean of group 3.
SD of group 3 (>0).
Size of group 3.
Results
5.9726
0.004416
At a glance:ANOVA: F = MSB/MSW, where MSB = SSB/(k−1) and MSW = SSW/(N−k).
Formula
F = (SSB/(k−1)) / (SSW/(N−k))
$$F = \frac{SSB/(k-1)}{SSW/(N-k)}$$How to Use
- Enter the means, standard deviations and sample sizes of the three groups.
- The calculator outputs the F statistic.
- Read the p-value.
- If p < 0.05, at least two group means differ significantly (post-hoc tests locate which pairs).
FAQ
What to do after ANOVA is significant?
The F-test only tells you that at least one group differs. To find which groups differ, run post-hoc tests (e.g. Tukey HSD).
What are ANOVA's assumptions?
Mainly that each group comes from a normal distribution, with homogeneity of variances (homoscedasticity) and independence. With large samples the normality assumption is less critical (central limit theorem).
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.