Three or more groups and an outcome that will not behave: ordinal, skewed, or driven by a few extreme values. What Kruskal-Wallis actually tests, when it is the right call, and how to report it in APA 7.
Kruskal-Wallis compares three or more independent groups on an outcome by working with ranks rather than raw values. Every observation in the combined sample is ranked from lowest to highest, and the test asks whether the ranks cluster differently across groups than chance would produce.
Because it uses ranks, a single extreme value cannot drag a group mean around, and the outcome does not have to be normally distributed. That is the whole appeal.
It is commonly described as a test of medians, and that is only true under an assumption most researchers do not check: that the groups have similarly shaped distributions. Strictly, Kruskal-Wallis tests whether one group tends to produce larger values than another. If the shapes differ, a significant result may reflect a difference in spread or skew rather than a shift in the center.
The result opens with four figures: H, labelled as a chi-square statistic, df, p, and eta squared as the effect.
Degrees of freedom are the number of groups minus one, so an outcome compared across six groups gives df = 5 regardless of sample size.
The eta squared figure is the one that stops a non-significant result being reported as inconclusive when it is actually a null. A comparison returning H = 4.58, df = 5, p = .470, eta squared = 0.000 is not ambiguous. There is nothing there.
A significant Kruskal-Wallis says the groups are not alike but does not say which pair differs, exactly as with ANOVA. Follow-up comparisons are a separate step and need their own error-rate control.
Reach for it when the outcome is ordinal, such as a single Likert item, when the distribution is badly skewed, or when a few extreme values would dominate a mean.
Do not reach for it reflexively because a normality test returned a small p. At larger sample sizes normality tests flag departures that ANOVA absorbs without difficulty, and the parametric test usually has more power. Quanta reports Kruskal-Wallis beside the classic F on every one-way ANOVA, so you can see whether the conclusion depends on the choice before committing to either.
Independence still applies. Ranks do not rescue a design where the same people appear in more than one group. For repeated measurements on the same people, use Friedman.
Watch the group sizes. Rank-based tests behave poorly with very small or very uneven groups, and the descriptives are where you see that before you interpret anything.
Lay the data out in long format: one row per person, one column holding the group label, one column holding the outcome.
Open Nonparametric & Categorical and select Kruskal-Wallis from the test list, then configure the variables in the Setup panel on the right. Results appear in the center.
Upload ordinal categories as text rather than numeric codes so the variable is typed as a category rather than a quantity.
Use the action bar to add the result to a report, copy the table, or copy the APA text.
Report H with its degrees of freedom, p, the effect size, and the group sizes. Give medians and an interquartile range rather than means.
A Kruskal-Wallis test found no difference in job performance across the six age groups, H(5) = 4.58, p = .470, η² = .00.
Report medians with an interquartile range, not means and standard deviations. A rank-based test paired with parametric descriptives is a mismatch reviewers notice.
Include the effect size. A non-significant H with eta squared at zero is a much stronger statement than a p value alone.
Describe the result as a difference in the tendency to produce larger values unless you have checked that the group distributions have similar shapes.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's correlation and nonparametric procedures are validated against R's cor and against hand-computed closed-form values, matched exactly. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Nonparametric is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
One-way ANOVA the parametric counterpart · Mann-Whitney U for exactly two groups · Friedman for repeated measures on the same people · the complete list on the analyses page.