One-way ANOVA calculator
Paste one group per line. You get F, both degrees of freedom, the p value, eta squared, and Levene's test for the assumption the pooled F depends on.
When to use this
A continuous outcome measured in three or more independent groups — a treatment, a control and a placebo arm; four sites; five education levels. Each row above is one group, and the values in a row are the cases in that group.
A worked example
Three groups of ten, means of 50.12, 55.00 and 57.96.
| Step | Result | Reading |
|---|---|---|
| One-way ANOVA | F(2, 27) = 37.81, p < .001 | Means differ |
| Effect size | η² = .737 | 73.7% of the variance is between groups |
| Levene's test | F(2, 27) = 0.15, p = .864 | Variances comparable |
The pooled F is appropriate here because the variances are close. If Levene's test had rejected, the equal-variance assumption behind that F would be in question.
Why not three t tests
Three groups means three pairwise comparisons, and each one carries its own 5% chance of a false positive. Three independent chances give a family-wise error rate of about 14.3%. With five groups it reaches 40%. ANOVA asks one question with one test, keeping the rate where you set it.
With exactly two groups the two procedures coincide: F is t², with the same p value. The t test page reports the same analysis with a mean difference and its confidence interval.
What a significant F does not tell you
It does not say which groups differ. That requires planned contrasts or a multiplicity correction such as Tukey's HSD or Holm's method. Running uncorrected pairwise t tests after a significant ANOVA gives back the error rate the ANOVA was protecting against.
What to report
F(2, 27) = 37.81, p < .001, η² = .74, with the group means and standard deviations, and a note that Levene's test was non-significant if you used the pooled test.
Frequently asked
Do the groups have to be the same size?
No. Equal sizes make the test slightly more robust when variances differ, but unequal groups are handled.
Which groups differ?
Not answered here. Use planned contrasts or a multiplicity correction.
What if the variances differ?
The pooled F becomes liberal. Report the Levene result and consider a Welch correction, which is not currently computed on this page.
Is the same people measured twice?
Then it is not a one-way ANOVA. Use repeated measures — the pairing changes the error term entirely.
When you have a file
The app reads the data file directly, builds the groups from a grouping variable, checks normality as well as variance, and exports the table.
Which test should I use? · t test calculator · chi-square calculator · ANOVA calculator · correlation calculator · p value calculator