One-Way ANOVA Calculator (Welch, Kruskal–Wallis)

Paste one line of numbers per group and get four tests side by side: the classic one-way ANOVA with its full table of sums of squares, Welch's ANOVA, the rank-based Kruskal–Wallis test, and the Brown–Forsythe version of Levene's test for equal spreads, together with η², ω² and a summary of each group. The example is R's PlantGrowth data, the set R documents its own aov function with, and it gives F = 4.846 on 2 and 27 degrees of freedom and p = 0.01591 here exactly as it does there, with Welch's F = 5.181 on 17.128 denominator degrees of freedom and a Kruskal–Wallis statistic of 7.9882. The reason to show all four is that they can disagree sharply. The classic F pools the variance of every group and assumes they are equal; when they are not, particularly with unequal group sizes, it can miss a large difference or report one that is not there. With a tight group of five, a scattered group of eight and a third of four, the classic test here gives F = 0.70 and p = 0.51 while Welch's gives F = 41.2 and p = 0.0002 — and Levene's test flags the unequal spreads at p = 0.003. So the tool reads Levene's result first and says which F it is going by. Kruskal–Wallis compares ranks rather than means, with the usual correction for ties, and is the one to lean on when groups are skewed or contain outliers. ω² is reported alongside η² because η² overstates the effect in small samples; ω² can come out slightly negative when the effect is essentially zero, and it is shown as computed rather than clipped. A significant result says only that some group differs; which ones need a post-hoc comparison such as Tukey's, which this tool does not perform.