One-Way ANOVA (Compare 3+ Group Means)

The member the t-test family was missing.

Run the calculator

Example

You enter

You get

Details, formula, and sources

Where a two-sample t-test compares two means, one-way ANOVA compares three or more at once. Paste each group on its own line (values separated by spaces or commas); it partitions the variation into between-groups SSB = sum n_i (mean_i - grand)^2 (df k-1) and within-groups SSW = sum (x - group mean)^2 (df N-k), then F = (SSB/(k-1))/(SSW/(N-k)) with the F-distribution p-value from the bundled special-function helper. Three classes scoring means of 89.2, 80.6, and 92.6 give F = 32.2 on 2 and 12 df, p = 1.5e-5 - the classes differ. Also reports eta^2 = SSB/SST (variance explained: 0.01 small, 0.06 medium, 0.14 large). Verified against scipy.stats.f_oneway. ANOVA flags THAT a difference exists, not which pair - a Tukey HSD post-hoc test locates it; assumes roughly normal groups with similar variances. A statistics aid; the study design governs.

SSB = sum n_i (mean_i - grand)^2 (df = k-1); SSW = sum sum (x - mean_i)^2 (df = N-k); F = (SSB/(k-1)) / (SSW/(N-k)); upper-tail p = I(x; df_w/2, df_b/2) the regularized incomplete beta with x = df_w/(df_w + df_b F); eta^2 = SSB/(SSB+SSW).

Per OpenIntro Statistics Chapter 7 (comparing many means with ANOVA), by name; the F-distribution p-value reuses the bundled regularized-incomplete-beta helper. Verified against scipy.stats.f_oneway.

Free at openintro.org; the F-test and its partition of variance are public-domain textbook statistics.

Estimate. AHJ and licensed professional govern.

Field names used by the API: groups_text, f_stat, eta_squared

Related tools