One Way Analysis of Variance (ANOVA) Calculator
A statistical test that compares the means of three or more independent groups to see if they are significantly different.
A clear F-Statistic and P-Value that tell you whether your groups actually differ — or the results just happened by chance.
4 values · mean 6.50 · range 5.00 – 8.00
4 values · mean 10.50 · range 9.00 – 12.00
4 values · mean 15.75 · range 14.00 – 18.00
F statistic
41.32
p = < 0.0001 · df (2, 9) · η² = large effect
Eta squared (η²)
0.9018
Effect size — large effect
SS between (signal)
172.17
Group averages vs the grand average
SS within (noise)
18.75
Natural variation inside groups
Significant difference — p = < 0.0001 < 0.05, and η² 0.9018 means 90.2% of the variation comes from the group factor. At least one group mean differs.
| Source | SS | df | MS | F | p |
|---|---|---|---|---|---|
| Between groups | 172.17 | 2 | 86.08 | 41.32 | < 0.0001 |
| Within groups | 18.75 | 9 | 2.08 | — | — |
| Total | 190.92 | 11 | — | — | — |
Group statistics
| Group | n | Mean | SD |
|---|---|---|---|
| Group 1 | 4 | 6.50 | 1.29 |
| Group 2 | 4 | 10.50 | 1.29 |
| Group 3 | 4 | 15.75 | 1.71 |
| Grand mean | 10.92 | ||
About this calculator
When you want to know whether three or more group means genuinely differ — plant yields under different fertilizers, sales across regions, test scores across teaching methods.
As the gatekeeper before pairwise comparisons: a significant F tells you at least one mean differs.
Formula
F = MS(between) ÷ MS(within)
How to use it
- 1
Enter each group's values in its own box — at least 2 values per group, 2 or more groups.
- 2
The calculator builds the full ANOVA table: sums of squares, degrees of freedom, mean squares, F and the exact p-value.
- 3
Use “Copy for Excel” to paste the whole table into a spreadsheet.
Example: three tidy groups
Groups {3,4,5}, {7,8,9}, {10,11,12} give SS-between 74, SS-within 6, F = 37 and p ≈ 0.0004 — a significant difference. Press “Reset to example” to reproduce every number.
In Excel: In Excel: Data → Data Analysis → Anova: Single Factor, or F.DIST.RT(F, df1, df2) for the p-value.