ANOVA Calculator
Compare the means of several groups at once with a one-way ANOVA. Enter the mean, standard deviation, and sample size for each group to get the F-statistic and sum-of-squares breakdown.
What This Calculator Does
One-way ANOVA (Analysis of Variance) tests whether the means of three or more independent groups are likely to be different from each other, using a single F-statistic instead of running many separate t-tests.
How the Math Works
The calculator splits the total variation in the data into two parts: variation between group means (SSB) and variation within each group (SSW). Each sum of squares is divided by its degrees of freedom to get a mean square (MSB and MSW), and the F-statistic is the ratio MSB / MSW. A large F suggests the group means differ more than random within-group noise would explain.
- SSB = sum of n_i × (group mean − grand mean)²
- SSW = sum of (n_i − 1) × (group standard deviation)²
- F = MSB / MSW
This tool is for general educational and planning use. To decide statistical significance, compare the resulting F-statistic to a critical value from an F-distribution table using the reported degrees of freedom, or consult a statistics reference.