ANOVA Calculator

This calculator runs a one-way ANOVA across three groups from each group's mean and sample size, plus a Pooled Variance figure you supply directly as Mean Square Within (line 32) — it never derives that variance from raw per-group standard deviations, because none are collected here. The Grand Mean is the sample-size-weighted average of the three group means (line 19); Mean Square Between sums each group's squared distance from that Grand Mean, weighted by its own sample size (lines 22-25), then divides by degrees-of-freedom-between, k − 1 = 2 for three groups (line 28). The F-Statistic is Mean Square Between divided by Mean Square Within (line 34), and the approximate p-value comes from a chi-square-to-normal approximation of the F-distribution rather than an exact F-table lookup.

At the defaults, F = 10.58 across 2 and 72 degrees of freedom, which the approximation reads as significant at α=0.05. Nudging each group's mean shows Group 3's mean — the one sitting furthest above the Grand Mean of 78.33 — moves the F-Statistic the most, while Group 1's mean, sitting below the Grand Mean, moves it the opposite way, because raising a below-average mean narrows rather than widens the between-group spread that line 22's sum of squares measures. What this does not account for: unequal-variance corrections such as Welch's ANOVA, post-hoc pairwise tests, and a literal 0 typed into Pooled Variance — that field reads `inputs.pooledVariance || 1` (line 10), so a real 0 is treated as missing and replaced with 1, never reaching the displayed 0.001 floor that Math.max applies after it.