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One-way ANOVA calculator

Tests whether the means of two or more independent groups differ. Returns the full ANOVA table (SS, df, MS, F, p) plus η² and group means.

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Paste one column of numbers per group (different sizes are fine) and rename the groups to match your conditions.

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When to use this

Use a one-way ANOVA when one categorical factor with two or more levels — teaching method, dosage group, region — divides your cases into independent groups, and you want to know whether the group means on a continuous outcome differ anywhere. It generalizes the independent t-test: instead of running every pairwise t-test (and inflating the Type I error rate), ANOVA performs a single F-test of the hypothesis that all group means are equal. A significant F tells you at least one mean differs; follow up with post-hoc tests (e.g. Tukey HSD) to find which pairs differ.

Key assumptions

  • Independent observations, with each case in exactly one group.
  • The outcome is approximately normal within each group (or group sizes are reasonably large).
  • Roughly equal variances across groups (homogeneity); with unequal variances consider Welch’s ANOVA.
  • Interval or ratio outcome; for ranks use Kruskal–Wallis.

Common mistakes

  • Stopping at the omnibus F — a significant ANOVA does not say which groups differ; run post-hoc comparisons.
  • Running multiple uncorrected t-tests instead of ANOVA in the first place.
  • Reporting F and p without η² (the share of variance explained by group membership).
  • Treating a repeated-measures design (same people in every condition) as between-groups — that needs repeated-measures ANOVA.

Frequently asked questions

My ANOVA is significant — which groups differ?
The omnibus F-test only says the means are not all equal. Compare the group-means table, then run post-hoc pairwise tests with a multiple-comparison correction (Tukey HSD, Bonferroni or Holm) to identify the specific differences.
How do I interpret η² (eta squared)?
η² is the proportion of total variance in the outcome explained by group membership. Common benchmarks: .01 small, .06 medium, .14 large. An η² of .12 means 12% of the variability in scores is attributable to the groups.
Can I use ANOVA with just two groups?
Yes — with two groups, one-way ANOVA and the (equal-variance) t-test are mathematically equivalent: F = t². Most people simply report the t-test in that case.

Related free tools

Sample size calculatorSample size for two groupsEffect size (Cohen's d)Descriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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