Perform one-way and two-way ANOVA with F-test visualization. Shows group means, within/between variance, and post-hoc tests.
This tool runs a one-way or two-way analysis of variance on group data entered as columns of numbers. It partitions total variance into between-group and within-group components, builds an F statistic from their mean squares, and reports the F ratio, degrees of freedom, and p-value alongside group means and a plotted spread. A common surprise: a low p-value only says the group means are not all equal - it does not say which groups differ, so a significant F should be followed by the built-in post-hoc pairwise test, not read on its own as an answer.
A concrete input and expected output from the current implementation.
Input
Group A: 4, 6, 8 Group B: 5, 7, 9 Group C: 8, 10, 12
Expected output
F(2, 6) = 3.25, p ≈ 0.111 (not significant at α = 0.05). Group means: A = 6, B = 7, C = 10; grand mean = 7.667. SSB = 26, SSW = 24; MSB = 13, MSW = 4.
Between-group mean square (13) divided by within-group mean square (4) gives F = 3.25; with 2 and 6 degrees of freedom that falls short of the 0.05 critical value of about 5.14, so the three means are not judged significantly different despite Group C's higher average.
For each group the tool computes the group mean, then splits total sum of squares into between-groups (SSB: each group mean's squared deviation from the grand mean, weighted by group size) and within-groups (SSW: each point's squared deviation from its own group mean). Dividing each by its degrees of freedom gives the mean squares used to form the F ratio MSB/MSW.
The tool also runs a post-hoc pairwise comparison step to flag which specific group pairs differ, using an adjustment intended to control the family-wise error rate - the chance of at least one false positive across the whole set of pairwise comparisons - rather than leaving each individual comparison at its own unadjusted significance level.
There's no universal minimum that applies to ANOVA in general. F tests run on very small groups are inherently unstable and low-powered, so with only a handful of observations per group, treat the resulting p-value as suggestive rather than a firm accept-or-reject, and add more observations per group where practical before relying on the result.
Not reliably. Standard one-way ANOVA assumes similar spread across groups; if one group's variance is much larger than another's, the F-test's error rate is no longer well controlled. In that situation a variance-robust alternative such as Welch's ANOVA is generally more appropriate, so treat results from groups with clearly unequal spread with caution.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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