ANOVA Calculator

Perform one-way ANOVA: compute SSB, SSW, F statistic and p-value for group means comparison.

About ANOVA Calculator

One-way ANOVA tests whether the means of multiple groups differ significantly. It partitions total variance into between-group (SSB) and within-group (SSW) components and computes an F ratio. A small p-value suggests at least one group mean differs.

Formula

F Statistic

F = MSB / MSW = (SSB/dfB) / (SSW/dfW)

MSB: Mean square between
MSW: Mean square within
dfB: k − 1
dfW: N − k

Worked example

With the default values below, ANOVA Calculator returns F Statistic of 18.7500. Change any input above and every figure here is recalculated in your browser.

Inputs used

Group 1 (comma separated): 23, 25, 27
Group 2 (comma separated): 30, 32, 28
Group 3 (comma separated): 35, 33, 37

Results

F Statistic: 18.7500
P-value: 0.002624
SS Between (SSB): 150.0000
SS Within (SSW): 24.0000
df Between: 2
df Within: 6

Step by step

1Values used
2F Statistic
3F Statistic= 18.7500
4P-value= 0.002624
5SS Between (SSB)= 150.0000
6SS Within (SSW)= 24.0000
7df Between= 2
8df Within= 6

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does a significant ANOVA tell you?

It tells you that at least one group mean differs from the others, but not which specific groups differ. Post-hoc tests (e.g., Tukey HSD) are needed for pairwise comparisons.

What assumptions does one-way ANOVA make?

Independence of observations, normality within groups, and approximately equal variances (homoscedasticity).