Math

ANOVA Calculator

Compare three or more groups and test for mean differences

Enter at least two groups to run ANOVA.

One-Way ANOVA Explained

One-way ANOVA compares the means of three or more groups by separating total variation into variation between groups and variation within groups. If the between-group variation is large relative to within-group noise, the F statistic becomes large and the p-value becomes small.

What The Calculator Returns

This calculator reports the F statistic, p-value, between-group and within-group degrees of freedom, eta squared, and a table of group means. That gives you both the hypothesis-test result and an effect-size summary.

Interpreting A Significant Result

A significant ANOVA tells you that at least one mean is different, but it does not identify which pair differs. If you need pairwise detail, follow up with planned contrasts or a post-hoc test such as Tukey's HSD.

Frequently Asked Questions

What does ANOVA test?
One-way ANOVA tests whether at least one group mean differs from the others. It does not tell you which specific pair differs; post-hoc testing is needed for that.
How should I format the group data?
Enter each group as a comma-separated list, and separate groups with a pipe character or a new line. For example: 12,14,18|15,16,20|19,21,23.
What is eta squared?
Eta squared measures the proportion of total variance explained by group membership. Larger values indicate a stronger between-group effect.
What assumptions does one-way ANOVA make?
ANOVA assumes independent observations, roughly normal errors within groups, and reasonably similar group variances. When those assumptions are badly violated, alternative tests may be more appropriate.

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