One-Way ANOVA Calculator (Two or Three Groups)
Paste each group’s values (leave the third group empty for two groups).
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One-Way ANOVA Calculator (Two or Three Groups) by TheCalcTools
How the One-Way ANOVA Calculator (Two or Three Groups) works
ANOVA compares the variation between group means with the variation within groups. F = (SS_between ÷ (k − 1)) ÷ (SS_within ÷ (N − k)). A large F means the group means are further apart than random scatter would explain.
A significant result says some means differ, not which ones; follow up with post-hoc tests such as Tukey’s HSD. ANOVA assumes roughly normal data with similar variances.
The formula
Worked example
Using the default values shown in the calculator:
| Group 1 | 85, 90, 78, 92, 88 |
|---|---|
| Group 2 | 75, 80, 72, 79, 83 |
| Group 3 (optional) | 90, 95, 91, 89, 96 |
| Significance level α | 0.05 |
- Three groups: F = 13.5808 with 2 and 12 degrees of freedom, p = 0.000828.
- At least one group mean differs (significant).
Result:
| F statistic | 13.5808 |
|---|---|
| p-value | 0.000828 |
| Degrees of freedom | 2 and 12 |
| Between-groups sum of squares | 526.933 |
| Within-groups sum of squares | 232.800 |
| Conclusion | At least one group mean differs (significant) |
Frequently asked questions
Is ANOVA with two groups the same as a t-test?
Yes: with two groups, F equals the square of Student’s pooled t, and the p-values match.
Sources and further reading
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