How to Report a Kruskal-Wallis Test in APA 7

The Kruskal-Wallis test is the non-parametric equivalent of a one-way ANOVA, and it reaches reviewers half-reported almost every time: an H with no degrees of freedom, no N, no effect size, and pairwise comparisons nobody corrected. Here is what the write-up needs, in what order, and what makes a reviewer stop. The wider picture on rank tests is in how to report non-parametric tests, and the parametric version in how to report an ANOVA.

What the write-up has to contain

Four required pieces and one that is required in practice. Required: the H statistic, its degrees of freedom, the p value and an effect size. The fifth is a description of each group with its median, interquartile range and n; without it the reader knows the groups differ but not in which direction.

Degrees of freedom are k − 1, where k is the number of groups: with three year groups, H(2). The total N sits inside the parentheses, as it does for chi-square, because H is evaluated against a χ² distribution on those same degrees of freedom. That gives the full form: H(2, N = 150) = 10.94, p = .004.

Report the n for each group as well, not just the total. Kruskal-Wallis handles unequal groups, but mean ranks depend on group size and nobody can recompute anything without those numbers. If one group has 12 participants and another has 80, that changes how the result should be read and it needs to be visible.

H, chi-square and what your software prints

Your software probably does not call it H. Through the legacy SPSS dialogs the Test Statistics table labels it Chi-Square; through the newer Nonparametric Tests route the model viewer calls it Kruskal-Wallis H. kruskal.test in R returns Kruskal-Wallis chi-squared; jamovi prints χ². Hence the most common question about this test: H or χ²? Both appear in print. H(2, N = 150) = 10.94 is the better choice because it names the test you actually ran, and if the journal insists on chi-square the value and degrees of freedom are identical. What you must not do is mix the two notations in one manuscript.

The H your software reports is already corrected for ties, and with Likert data that matters. If your outcome has five possible values and 150 respondents, ties are everywhere and the correction lifts the statistic noticeably. Do not recompute H by hand from the textbook formula to check the output: the two will disagree, and the corrected one is the one to publish.

With small groups — the most cited convention is a minimum of five cases per group, and below that the χ² approximation gets crude — ask for an exact or Monte Carlo p value instead. If you do, say so. One sentence in the analysis plan (“exact significance was used given the small group sizes”) saves an entire round of review.

Effect size: epsilon squared and eta squared H

The most widely used is epsilon squared, and the arithmetic fits on a phone: ε² = H / (N − 1). With H = 10.94 and N = 150 that gives ε² = .07. It ranges from 0 to 1 and reads as the proportion of variability in the ranks accounted for by group membership.

The alternative is eta squared based on H: η²_H = (H − k + 1) / (N − k), which on the same data returns .06. Either is defensible and one is enough, provided you say which. People usually borrow Cohen’s η² benchmarks to interpret them (.01, .06, .14), but those were derived for a different statistic: treat them as orientation, not as a verdict.

Formatting, which is where most manuscripts slip: epsilon and eta are Greek letters, so they are set upright and never italicized. Because neither can exceed 1, neither takes a leading zero — ε² = .07, not 0.07. H, N, p and z are italicized.

A worked example

“Psychological distress differed across the three year groups (n = 50 per group). Scores were highest among final-year students (Mdn = 26.0, IQR = 21.0–31.0, mean rank = 90.30), followed by third-year students (Mdn = 23.0, IQR = 19.0–28.0, mean rank = 74.60) and first-year students (Mdn = 21.0, IQR = 17.0–26.0, mean rank = 61.60). A Kruskal-Wallis test indicated a significant difference between year groups, H(2, N = 150) = 10.94, p = .004, ε² = .07. Dunn’s pairwise comparisons with Bonferroni adjustment located the difference between final-year and first-year students, z = 3.30, p = .003; neither remaining comparison reached significance (final-year vs. third-year, z = 1.81, p = .212; third-year vs. first-year, z = 1.50, p = .404). A rank-based test was used because distress scores were strongly right-skewed in all three groups.”

The order is not arbitrary: descriptives with medians first, then the omnibus test, then the effect size, then the corrected pairwise comparisons, and last the sentence explaining why a rank test at all. That final sentence is the one almost everyone omits, and it is what stops a reviewer asking why you did not run an ANOVA.

If what you are staring at is the SPSS pair of tables — Ranks and Test Statistics — plus the pairwise comparison chart, and you cannot tell which figure goes where, paste the output into the interpreter and it hands it back in exactly this format.

Already drafted it? Paste your Results section into Review one section and you get the first objection a reviewer would raise, quoting the exact sentence from your text. Free, no sign-up.

Pairwise comparisons: Dunn, not three Mann-Whitneys

H tells you that some group differs from some other, not which. That is what pairwise comparisons are for, and the standard is Dunn’s test, which reuses the ranks from the overall analysis instead of re-ranking within each pair. For every comparison report the standardized test statistic z, the adjusted p value and which correction you applied.

SPSS gives these in the pairwise comparisons table with two significance columns, Sig. and Adj. Sig. The one that goes in the manuscript is the adjusted one, and the note has to say the adjustment is Bonferroni. If you prefer Holm or Benjamini-Hochberg — less conservative and entirely defensible — you have them in R via dunn.test or PMCMRplus, but then name them in the text.

What you cannot do is run every Mann-Whitney the design allows and correct nothing. Three groups mean 3 comparisons; five groups mean 10, and by then the chance of at least one false positive is close to 40%. If you are going to report pairwise tests that way, see how to report a Mann-Whitney U test and adjust the p values afterwards.

A working rule: run the pairwise tests only if H is significant. It is not a law — some methodologists argue for going straight to a small set of planned comparisons — but it is what most reviewers expect, and skipping the omnibus test is something you argue for in the analysis plan, not in the response letter.

What reviewers flag

Describing groups with means. If you chose a rank test because the mean does not represent your data well, describing the groups with M and SD two lines later contradicts you. Medians and interquartile ranges.

Writing “medians differed significantly”. Kruskal-Wallis tests medians only when the group distributions share the same shape. In general it tests whether one group tends to produce larger values than another, which is a broader hypothesis. Look at the histograms by group before you write that sentence.

H without degrees of freedom or without N. Neither the reader nor an automated checker can recompute the p value without them, and statcheck-style tools flag exactly that.

Uncorrected pairwise tests, or corrected without saying how. “Post hoc comparisons were conducted” carries no information. Name the correction and show the adjusted p values.

Using it on repeated measures. If your three “groups” are three time points from the same participants, the test is Friedman’s. Independence of observations is the assumption Kruskal-Wallis genuinely requires, and that one is not negotiable.

Choosing it purely because Shapiro-Wilk came out significant. In large samples that test detects departures too small to matter, while ANOVA copes reasonably well with them. The decision comes from the distribution and the group sizes, as I explain in why Shapiro-Wilk gets misread.

Frequently asked questions

How do you report a Kruskal-Wallis test in APA 7?

With the H statistic, its degrees of freedom, the total N and the p value, in this form: H(2, N = 150) = 10.94, p = .004. An effect size goes alongside it, usually epsilon squared, and the group descriptives with medians and interquartile ranges come first. If the omnibus test is significant, add the pairwise comparisons with their correction.

Does the Kruskal-Wallis H have degrees of freedom?

Yes, k − 1, where k is the number of groups: three groups give H(2). It is standard to include the total N inside the parentheses as well, exactly as for chi-square, because H is evaluated against a chi-square distribution on those degrees of freedom. Without df and N nobody can recompute your p value.

What effect size do you report with Kruskal-Wallis?

Epsilon squared is the most common: ε² = H / (N − 1), ranging from 0 to 1 and read as the proportion of variability in the ranks accounted for by group membership. The alternative is eta squared based on H: (H − k + 1) / (N − k). Either works as long as you say which one you used; reporting none is what gets flagged.

Which post hoc test follows a Kruskal-Wallis?

Dunn’s test with a correction for multiple comparisons, because it reuses the ranks from the overall analysis. For each comparison report the standardized test statistic z, the adjusted p value and the correction applied. In SPSS the column that belongs in the manuscript is Adj. Sig., not the unadjusted significance.

Does Kruskal-Wallis compare means, medians or ranks?

It compares ranks. It becomes a test of medians only when the group distributions have the same shape; in general it tests whether one group tends to produce larger values than the others. That is why groups are described with medians and interquartile ranges, and why many authors add each group’s mean rank.

When should I use Kruskal-Wallis instead of a one-way ANOVA?

Use it when the outcome is ordinal, when the distribution is heavily skewed, or when groups are small and contain outliers you cannot justify removing. ANOVA is fairly robust to moderate departures from normality with balanced groups, so defaulting to the rank test costs power. Make the decision before you look at any p value and explain it in the method.

With H, its degrees of freedom, the N, an effect size and properly corrected pairwise comparisons, your Kruskal-Wallis is reported the way APA 7 expects. If the design gets harder — badly unbalanced groups, covariates, repeated measures within each group — we can work through it together in my statistical consulting.