One-Way ANOVA Calculator

Ordinary one-way ANOVA for independent groups with a numerical outcome. This does not run Welch’s ANOVA or post-hoc comparisons.

Load worked example

Group measurements (one group per line)

Separate values with commas or spaces. Groups may have different sizes; each needs at least two observations.

Significance level (α)0.100.050.01

Run ANOVAClear

Compare a numerical outcome across independent groups

Enter one group per line, separating measurements with commas or spaces. Each group needs at least two finite values. Groups can have different sizes. The calculator performs ordinary one-way ANOVA, assuming independent observations, roughly normal model errors and equal population variances.

Repeated measurements, matched groups or clustered observations need an appropriate design and analysis. Unequal variance problems may call for Welch’s ANOVA. This tool does not run Welch’s ANOVA, post-hoc comparisons, repeated-measures analysis or factorial ANOVA.

Reproduce the worked example

Load three hypothetical groups: 2,3,4, 4,5,6, 6,7,8. Their means are 3, 5 and 7, each sample SD is 1, and the overall mean is 5. The data are also available as a downloadable CSV.

Between-group sum of squares is 3(3−5)²+3(5−5)²+3(7−5)²=24. Within-group sum of squares is 6. Divide by df₁=2 and df₂=6 to obtain mean squares 12 and 1, giving F=12.0000 and p=0.0080. Sample η²=24/(24+6)=0.8000.

The upper-tail F test gives evidence against equal population means at α=0.05 under the assumptions. It does not establish which pairs differ, that every pair differs, or a causal effect. η² describes the fraction of sample variation accounted for by group means, not the percentage of individual outcomes caused by the grouping.

Use the output responsibly

Inspect observations, group spreads, collection design and residual structure. Do not rely solely on a preliminary variance test to justify a method. A small dataset may conceal departures that a test cannot detect, and a non-significant overall result does not prove equivalence.

For reporting, include group labels, sizes, means and SDs, the F statistic, both degrees of freedom, p-value, a suitable effect summary, and design limitations. If you follow with pairwise comparisons, choose an appropriate multiplicity adjustment and report their uncertainty; this calculator does not supply those intervals.

Continue

Read the ANOVA lesson, look up an F critical value, or practice a complete analysis. NIST explains the ANOVA sums of squares and reference test.