ANOVA Calculator
Determine whether group means differ significantly by comparing between-group and within-group variability using the F-test.
How to Use This Calculator
Summarize variability
Calculate the sum of squares between groups (SSB) and within groups (SSW) from your dataset.
Enter degrees of freedom
Provide dfB = k − 1 for k groups and dfW = N − k for the total sample size N.
Run the calculation
Click “Calculate F-Statistic” to compute the mean squares and the resulting F value.
Compare to critical value
Use an F-distribution table or calculator with dfB and dfW to decide if the result is statistically significant.
Formula
- SSB: Sum of squares between groups measuring variability of group means around the grand mean.
- SSW: Sum of squares within groups measuring variability inside each group.
- dfB: Between-group degrees of freedom (number of groups minus 1).
- dfW: Within-group degrees of freedom (total observations minus number of groups).
Full Description
Analysis of variance (ANOVA) is used to test whether the means of three or more groups are equal. It decomposes total variability into variability explained by group membership (between-group) and residual variability (within-group). The F-statistic quantifies how much larger the between-group variability is relative to the within-group variability. A large F value indicates that the group means differ more than would be expected by random sampling variation alone.
This calculator helps you perform the classic one-way ANOVA F-test by turning sums of squares and degrees of freedom into mean squares and the final F ratio. After calculating the F value, compare it against the critical value from the F-distribution (or compute a p-value) to determine whether to reject the null hypothesis that all group means are equal.
Frequently Asked Questions
When should I use ANOVA instead of a t-test?
Use ANOVA when you have three or more group means to compare. It extends the independent-samples t-test to multiple groups without inflating the Type I error rate.
How do I find the p-value from the F-statistic?
You can use an F-distribution table or an online critical value calculator. Provide the calculated F value along with dfB and dfW to obtain the p-value.
What assumptions does ANOVA rely on?
ANOVA assumes independent observations, normally distributed residuals, and equal variances across groups (homoscedasticity). Consider alternative tests if these assumptions are severely violated.
Can I use this calculator for repeated-measures ANOVA?
This tool is designed for one-way independent-groups ANOVA. Repeated-measures designs require different sums of squares and should be analyzed with a dedicated repeated-measures approach.