The Kruskal-Wallis H test is the non-parametric alternative to the one-way ANOVA: it compares three or more independent groups on ranks when the data are ordinal or the normality assumption fails. Because it works on ranks, the APA 7 write-up uses medians and the H statistic, and people often report the wrong summary values. This guide gives you the exact format, a worked example you can copy, and the mistakes reviewers catch.
What you need before you write a single word
An APA 7 write-up of a Kruskal-Wallis test needs these values from your output:
- The median (Mdn) for each group. Report medians, not means.
- The H statistic (some software labels it chi-square, because H is distributed approximately as chi-square).
- The degrees of freedom (df), which is the number of groups minus 1.
- The exact p value.
- An effect size, usually epsilon squared or eta squared based on the H statistic.
- Post hoc comparisons (for example Dunn's test with a correction) if H is significant and you need to say which groups differ.
The APA 7 format template
Report the omnibus result in running text using this pattern:
A Kruskal-Wallis test showed a significant difference in [dependent variable] across [groups], H(df) = X.XX, p = .XXX, ε² = .XX.
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Formatting rules reviewers actually check:
- Report medians for each group, not means and standard deviations.
- Put the degrees of freedom (groups minus 1) in parentheses after H.
- No leading zero on p or on the effect size.
- Round H to two decimals. If p is below .001, write p < .001.
- If H is significant, follow up with post hoc tests and report which groups differ.
A worked example
Suppose you compared satisfaction ratings (1 to 10, ordinal) across three store locations.
- Location A (n = 25): Mdn = 6
- Location B (n = 27): Mdn = 8
- Location C (n = 24): Mdn = 5
- Omnibus result: H(2) = 11.42, p = .003, ε² = .15
Written up in APA 7, that becomes:
A Kruskal-Wallis test showed a significant difference in satisfaction ratings across the three locations, H(2) = 11.42, p = .003, ε² = .15. Dunn's post hoc tests with a Bonferroni correction indicated that Location B (Mdn = 8) was rated significantly higher than Location C (Mdn = 5), p = .002. No other pairwise comparison was significant.
The APA 7 table (recommended)
Because there are three or more groups, a medians table earns its place. APA tables use horizontal rules only:
| Location | n | Mdn |
|---|---|---|
| A | 25 | 6 |
| B | 27 | 8 |
| C | 24 | 5 |
Note. Satisfaction rated on a 1 to 10 scale. The difference was significant, H(2) = 11.42, p = .003, ε² = .15.
Reporting a non-significant result
Use the same statistics; change the wording, and do not call it a trend:
A Kruskal-Wallis test found no significant difference in satisfaction ratings across the three locations, H(2) = 3.04, p = .219, ε² = .04. No post hoc tests were carried out.
Where to find these numbers in SPSS
- Ranks: N and mean rank per group (report medians from Explore instead).
- Test Statistics: Kruskal-Wallis H (labelled Chi-Square in older versions), df and Asymp. Sig.
- Pairwise comparisons (Dunn's tests with adjusted Sig.) come from the newer Nonparametric Tests > Independent Samples dialog.
Mistakes reviewers catch
- Reporting means and SDs. The test ranks the data, so report medians.
- Stopping at the omnibus test. A significant H says the groups are not all equal; run and report post hoc tests (Dunn's test) to say which differ.
- Using it on paired data. For three or more related conditions from the same participants use the Friedman test, not Kruskal-Wallis.
- No effect size. Report epsilon squared or eta squared based on H.
- Writing p = .000. Report p < .001.
When to use it instead of a one-way ANOVA
Use the Kruskal-Wallis test when:
- The dependent variable is ordinal, or
- It is continuous but badly non-normal within groups, especially in small samples, or
- Extreme outliers would distort group means.
If the ANOVA assumptions hold, that test is more powerful. See our guide on reporting a one-way ANOVA.
Let KyroStat do the write-up for you
Formatting a rank-based omnibus test, with medians, the H statistic, and post hoc comparisons, is where errors creep in. KyroStat runs the Kruskal-Wallis test on your data, reports the medians, runs the post hoc comparisons, and hands you the finished APA 7 sentences and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.
Frequently asked questions
Should I report means or medians for a Kruskal-Wallis test? Medians. The test works on ranks, so medians describe the groups appropriately.
What is the H statistic? The Kruskal-Wallis test statistic. It is distributed approximately as chi-square with degrees of freedom equal to the number of groups minus 1, which is why some software labels it chi-square.
Which post hoc test should I use? Dunn's test with a Bonferroni or Holm correction is the usual choice after a significant Kruskal-Wallis result.
My p value shows as .000. What do I write? Report p < .001. A p value is never exactly zero.
Which related guides might I need? Often these: post hoc tests, Welch's ANOVA and descriptive statistics.