The Kruskal-Wallis H test compares three or more independent groups when the outcome is ordinal or too skewed for a one-way ANOVA. SPSS prints two main sets of tables: the legacy Ranks and Test Statistics tables, and the newer Independent-Samples Kruskal-Wallis output with Hypothesis Test Summary and Dunn's pairwise comparisons. This guide reads both row by row with a worked example, flags the misreadings that cost marks, and gives the APA 7 write-up. For the reporting format on its own, see the Kruskal-Wallis APA guide.
What SPSS gives you
Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples, with Kruskal-Wallis H ticked, produces:
- Ranks: N, mean rank and sum of ranks for each group.
- Test Statistics: Kruskal-Wallis H, degrees of freedom and the p value.
Analyze > Nonparametric Tests > Independent Samples (the newer procedure) gives:
- Hypothesis Test Summary: a summary statement and decision.
- Pairwise Comparisons: Dunn's test results for every pair of groups, with adjusted p values.
Neither procedure prints the medians you report. The legacy dialog can show them via Options > Descriptive (check Quartiles). For more detail, use Analyze > Descriptive Statistics > Explore with the grouping variable as Factor.
The worked example
Sixty-three participants rated their satisfaction (1 to 10 scale, ordinal) with one of three retail locations. Group A (n = 20), Group B (n = 22) and Group C (n = 21). All numbers below come from one dataset.
From Explore: Group A Mdn = 2; Group B Mdn = 6; Group C Mdn = 3.
Table 1: Ranks
| Group | N | Mean Rank | Sum of Ranks |
|---|---|---|---|
| Group A | 20 | 24.70 | 494.00 |
| Group B | 22 | 44.07 | 969.50 |
| Group C | 21 | 26.31 | 552.50 |
| Total | 63 |
SPSS ranks all 63 ratings together from lowest (rank 1) to highest (rank 63), giving tied ratings the average of their ranks, then adds the ranks up by group.
- N: 20, 22 and 21 participants per location.
- Mean Rank: 24.70 for Group A, 44.07 for Group B, 26.31 for Group C. Higher mean ranks mean higher ratings. Group B had the highest mean rank (44.07), so that location tended to be rated highest. This is how you read the direction.
- Sum of Ranks: 494.00, 969.50 and 552.50. They always add up to N(N + 1)/2 = 63 × 64 / 2 = 2016.
Mean ranks are not medians and are not in the units of the scale. Use them for direction and report the medians.
Table 2: Test Statistics
| Score | |
|---|---|
| Kruskal-Wallis H | 15.098 |
| df | 2 |
| Asymp. Sig. (2-tailed) | .001 |
- Kruskal-Wallis H = 15.098: the test statistic you report. It is computed from the ranks and is distributed approximately as chi-square with df equal to the number of groups minus 1. (Older SPSS versions label this row "Chi-Square" instead; it is the same number.) With no difference between groups, H would be small.
- df = 2: the number of groups minus 1. You report this as H(2).
- Asymp. Sig. (2-tailed) = .001: the two-sided p value from the chi-square approximation. This is the p you report.
If you request an Exact test, SPSS may add an Exact Sig. row. If so, say which p value (asymptotic or exact) you report.
The effect size SPSS does not print
Compute epsilon squared from H and the total sample size (N): ε² = H / (N − 1) = 15.098 / 62 = .24. This indicates a relatively strong effect (Rea and Parker).
Some researchers report eta squared H instead: η²H = (H − k + 1) / (N − k), where k is the number of groups. For this example, η²H = (15.098 − 3 + 1) / (63 − 3) = 13.098 / 60 = .22. By common benchmarks for eta squared (.01 small, .06 medium, .14 large), that is also a large effect. Either epsilon squared or eta squared H is acceptable; say which you use.
The newer Nonparametric Tests output
The Independent Samples procedure (not Legacy Dialogs) starts with a Hypothesis Test Summary that names the null hypothesis, the test, gives the p value and makes a recommendation ("Reject the null hypothesis" or "Retain the null hypothesis"). To see the Pairwise Comparisons table with Dunn's test results, double-click the Hypothesis Test Summary to open the Model Viewer, then choose Pairwise Comparisons from the View list (the wording and menu may differ between SPSS versions).
Table 3: Hypothesis Test Summary
| Null Hypothesis | Test | Sig. | Decision |
|---|---|---|---|
| The distribution of Score is the same across categories of Group | Independent-Samples Kruskal-Wallis Test | .001 | Reject the null hypothesis |
- Null Hypothesis: the formal statement being tested.
- Sig.: the same p value as the Test Statistics table.
- Decision: "Reject the null hypothesis" if p < .05, otherwise "Retain the null hypothesis". This is not a write-up; report the statistics and the conclusion in your own words.
Table 4: Pairwise Comparisons (Dunn's Test)
| Sample 1-Sample 2 | Test Statistic | Std. Error | Std. Test Statistic | Sig. | Adj. Sig.ᵃ |
|---|---|---|---|---|---|
| Group A-Group B | −19.368 | 5.594 | −3.462 | .001 | .002 |
| Group A-Group C | −1.610 | 5.657 | −.285 | .776 | 1.000 |
| Group B-Group C | 17.759 | 5.524 | 3.215 | .001 | .004 |
ᵃ Significance values have been adjusted by the Bonferroni correction for multiple tests.
- Sample 1-Sample 2: the two groups being compared.
- Test Statistic: the difference in mean ranks for this pair, signed. A negative value means the first group had a lower mean rank.
- Std. Error: the standard error for this pair, using a variance corrected for ties.
- Std. Test Statistic: the test statistic divided by the standard error; this is the signed z-score.
- Sig.: the two-sided p value before any adjustment for multiple comparisons. This is the raw p value.
- Adj. Sig.: the p value after Bonferroni adjustment. This is the value you report.
Read once per pair: Group B (mean rank 44.07) was rated significantly higher than both Group A (mean rank 24.70) and Group C (mean rank 26.31); Groups A and C did not differ.
Misreadings that cost marks
- Reporting mean ranks as if they were medians. Report medians (and IQRs) from Explore; use mean ranks only for direction.
- Forgetting the effect size. SPSS does not print one, so compute epsilon squared ε² = H / (N − 1).
- Stopping at the omnibus test. A significant H says the distributions are not all equal; run and report Dunn's post hoc tests to say which pairs differ.
- Adjusting Dunn's p values a second time. Dunn's test p values in the Adj. Sig. column are already corrected for multiple comparisons; report them directly without further adjustment.
- Writing p = .000. Write p < .001.
- Forgetting to report df in parentheses after H. Write H(k − 1), for example H(2) = 15.10.
The APA 7 format template
A Kruskal-Wallis test showed a significant difference in [dependent variable] across [groups], H(df) = X.XX, p = .XXX, ε² = .XX.
If H is significant, follow with post hoc comparisons:
Dunn's post hoc tests with a Bonferroni correction indicated that [group 1] (Mdn = X) was rated significantly higher than [group 2] (Mdn = X), p = .XXX. [Group 3] (Mdn = X) did not differ from either group.
The write-up for this example
A Kruskal-Wallis test showed a significant difference in satisfaction ratings across the three locations, H(2) = 15.10, p < .001, ε² = .24. Dunn's post hoc tests with a Bonferroni correction indicated that Group B (Mdn = 6) was rated significantly higher than both Group A (Mdn = 2), p = .002, and Group C (Mdn = 3), p = .004. Group A and Group C did not differ significantly, p > .999.
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Frequently asked questions
Do I report the mean ranks or the medians? Medians. The test works on ranks, so medians describe the groups in the scale's units. Use mean ranks only to understand which group tended higher.
What is the H statistic? The Kruskal-Wallis test statistic. It is distributed approximately as chi-square with df equal to the number of groups minus 1.
How do I get the effect size? SPSS does not print one. Compute epsilon squared: ε² = H / (N − 1), where N is the total sample size. Alternatively, some papers report eta squared H: η²H = (H − k + 1) / (N − k), where k is the number of groups. Either is acceptable.
What if the test is significant but no Dunn post hoc is? It can happen with borderline omnibus p values. Report both results honestly.
Which post hoc test should I use? Dunn's test with Bonferroni or Holm correction. SPSS's Independent Samples procedure gives it automatically.
Why are the older and newer procedures different? The legacy procedure (K Independent Samples) prints H and a simple p value. The newer Independent Samples procedure adds a hypothesis test summary and Dunn's pairwise tests. Both are correct; the newer one gives more detail.
Which related guides might I need? Often these: one-way ANOVA output (the parametric alternative), post hoc tests, and how to report a Kruskal-Wallis test in APA 7.