ANOVA Calculator
Whether three or more groups really differ, by comparing the variation between them against the variation inside them.
Results
What this tool does
When you have three treatments, four suppliers or five classes, comparing them two at a time multiplies your chance of a false alarm. One-way analysis of variance asks the question once. It splits the total variation into the part that comes from which group a value is in and the part that is just noise inside each group, and the ratio of the two is the answer. Write one group per line with a name and its values, and this page gives you the F ratio, the p value, and the share of the variation that the grouping actually explains.
Formula
F = (between-group variation ÷ between df) ÷ (within-group variation ÷ within df)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
groups | The groups, one per line: name = values | — |
alpha | Significance level | % |
OUT | F | — |
PV | p value | — |
VD | What that means | — |
TB | The groups | — |
D1 | Degrees of freedom, between groups | — |
D2 | Degrees of freedom, within groups | — |
CR | The value it had to beat | — |
ET | Of the variation the grouping explains | % |
NG | Groups | — |
CT | Count | — |
GM | Mean of everything | — |
Worked example
- The groups, one per line: name = valuesMethod A = 12, 15, 11, 19, 14 Method B = 18, 21, 17, 24, 20 Method C = 9, 14, 10, 12, 11
- Significance level5 %
- F14.3636
- p value0.000654
- What that meansThe difference is bigger than chance would give
- The groupsMethod A n=5 m=14.2000 sd=3.1145 Method B n=5 m=20 sd=2.7386 Method C n=5 m=11.2000 sd=1.9235
- Degrees of freedom, between groups2
- Degrees of freedom, within groups12
- The value it had to beat3.8853
- Of the variation the grouping explains70.54 %
- Groups3
- Count15
- Mean of everything15.1333
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
Frequently asked questions
Why not just run a t-test on every pair?
Because each test carries its own chance of a false alarm, and they stack up. With three groups there are three pairs; with five there are ten. At the usual five per cent threshold, ten tests give you about a forty per cent chance of finding at least one difference that is not there. ANOVA asks the single question — is any group different from the others — with one test and one error rate. If it says yes, that is the point at which comparing individual pairs becomes reasonable, with a correction for how many you run.
It says yes — which group is the different one?
This test cannot tell you, and that is not a shortcoming of the page but of the method. ANOVA answers one question: are all these groups the same, yes or no. Finding out which one stands out needs a follow-up — Tukey's honestly significant difference is the usual choice — that compares the pairs while controlling the false alarm rate across all of them. The group summary above gives you the means and spreads, which is usually enough to see where to look.