ANOVA comparison workspace
Compare 2 to 20 group means with one-way ANOVA, Welch's ANOVA and Tukey, Games-Howell or adjusted pairwise follow-up comparisons, or run a two-way ANOVA with Type II or Type III sums of squares.
Runs locally in your browser in a background worker; nothing is uploaded. CSV up to 1,000,000 characters and 10,000 data rows, 2 to 20 groups with at least 2 observations each and group names of at most 80 characters. Summary CSV headers are group,n,mean,sd. Two-way ANOVA needs raw data and at most 20 levels per factor. Confidence level 0.5 to 0.9999. Setting numbers are plain decimals with a digit before the point, such as 0.95, without exponents. In CSV with two or more columns a blank line between rows is rejected, and in one-column CSV it is a blank cell; blank lines after the last row are ignored. Downloads: a JSON report, CSV tables (ANOVA, pairwise comparisons, groups, checks, residuals and QQ points) and SVG charts. Paste one row per observation with a group column and a numeric value column. Up to 1,000,000 characters. Review the settings before running.
Your result
How to use ANOVA comparison workspace
- Paste long-format CSV with one row per observation, or a summary CSV with group,n,mean,sd.
- Name the group and value columns, and a second factor column if you want a two-way ANOVA.
- Choose the follow-up comparisons and the confidence level.
- Run the analysis, check the variance tests and residual QQ chart, and download the report.
Useful next steps
One-way ANOVA
The F test compares the variance between group means with the variance within groups. Eta squared and omega squared describe the share of variance explained. Welch's ANOVA (Welch 1951, Biometrika 38:330) is reported beside it because it does not assume equal variances. Levene's test and the Brown-Forsythe test (Brown and Forsythe 1974, JASA 69:364) check the spread; both are left out when every group is constant or holds two values equally often (for example two values per group), because the absolute deviations then do not vary within groups and the tests are undefined. Residuals are shown on a normal QQ chart.
Follow-up comparisons
Tukey HSD uses the studentized range with the Tukey-Kramer standard error for unequal sizes (Tukey 1953; Kramer 1956, Biometrics 12:307). Games-Howell uses separate variances and Welch degrees of freedom (Games and Howell 1976, Journal of Educational Statistics 1:113). Both give simultaneous confidence intervals. Pairwise t tests use the pooled variance with Holm (Holm 1979, Scandinavian Journal of Statistics 6:65) or Bonferroni adjusted p-values. Differences are listed as later group minus earlier group, as in R TukeyHSD.
Two-way ANOVA
With a second factor the model includes both main effects and their interaction, using sum-to-zero coding. In unbalanced designs Type II and Type III sums of squares answer different questions and can disagree (Langsrud 2003, Statistics and Computing 13:163), so the chosen type is labelled. Empty cells cannot be fitted with an interaction.
Limits
ANOVA assumes independent observations. With very unequal variances and sizes, prefer Welch's ANOVA with Games-Howell comparisons. Repeated measures are not supported; use the Friedman test in the nonparametric workspace.