One-Way ANOVA Calculator

Test whether the means of k ≥ 2 independent groups are equal. Paste your data, see the F-statistic, the upper-tail p-value via the F-distribution, the full ANOVA decomposition (SSB, SSW, MSB, MSW), the per-group n / mean / SD, and the η² / ω² effect sizes. Pure client-side, no upload, no tracking.

Group data

One group per line. Optional label before a colon. Tokens split on whitespace or commas. Non-numeric tokens are dropped. Lines beginning with # are comments.

Result

F-statistic — df = —
p-value — P(Fdf1,df2 ≥ F)
Conclusion —

ANOVA decomposition

Source SS df MS F p
Between groups — — — — —
Within groups — — —
Total — — — — —

Per-group summary

Effect size

η² (eta-squared) — SSB / SST
ω² (omega-squared) — less biased than η²
Cohen's f — sqrt(η² / (1 − η²))

—

F-critical reference

Critical values Fα, df1, df2 such that P(F ≥ Fα) = α. If your F-statistic is greater than the α = 0.05 critical value, you reject the null at the 5% level.

α Fcrit Verdict
0.10——
0.05——
0.01——
0.001——
How this works — assumptions, formula, caveats

One-way ANOVA partitions the total sum of squared deviations from the grand mean (SST) into two parts: the variation explained by group membership (SSB) and the residual variation within groups (SSW). The test statistic

F = (SSB / (k − 1)) / (SSW / (N − k)) = MSB / MSW

follows the F-distribution with (k − 1, N − k) degrees of freedom under the null hypothesis that all group means are equal. The p-value is the upper-tail probability P(Fdf1,df2 ≥ F), computed via the regularised incomplete beta function Ix(df2/2, df1/2).

Assumptions

  • Independence — observations across and within groups are independent.
  • Normality — the residuals are approximately normally distributed (check with a histogram or a Shapiro–Wilk test for small samples).
  • Homogeneity of variance — the within-group variances are roughly equal (check with Levene’s or Brown–Forsythe; the Welch ANOVA is more robust when this is violated).

Reading the effect sizes

  • η² (eta-squared) = SSB / SST. The proportion of total variance explained by group membership. Slightly biased upward.
  • ω² (omega-squared) = (SSB − df1 · MSW) / (SST + MSW). A less biased estimator.
  • Cohen’s f = sqrt(η² / (1 − η²)). Conventional benchmarks: 0.10 small, 0.25 medium, 0.40 large.

Post-hoc comparisons

When the F-test rejects the null, follow up with pairwise comparisons (Tukey’s HSD, Bonferroni, or Holm) to find which groups differ. ANOVA answers “are all means equal?”; it does not tell you which pairs drive the difference.

Pure client-side math. The page computes the regularised incomplete beta function via the continued-fraction form of Numerical Recipes 6.4, accurate to ~10−12.