METHOD GUIDE
Kruskal-Wallis Test in SPSS
Adjusted Pairwise Comparisons and Effect Size
The omnibus result says only that the groups are not all alike. SPSS can add adjusted pairwise comparisons, but it prints no effect size, so both the follow-up and the size of the difference have to be planned.
IN SHORT
What the Omnibus Result Does and Does Not Tell You
A Kruskal-Wallis test compares three or more independent groups through the ranks of an ordinal or continuous outcome, and asks whether values in some groups tend to be larger than in others. A significant result does not say which groups differ, and it supports a statement about medians only when the distributions have the same shape. To run the Kruskal-Wallis test in SPSS, open Analyze, Nonparametric Tests, Independent Samples, assign the outcome and the grouping variable, choose the test for k samples, and request all pairwise multiple comparisons so that the follow-up is adjusted. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
An omnibus H opens the analysis and does not finish it. Support for the full rank-based comparison on your data, and for a comparison of means where the question is about means, is described here.
Kruskal-Wallis Test
The rank-based comparison of three or more independent groups carried out within your study design, with the pairwise follow-up, the effect size and the reporting agreed for your data.
One-Way ANOVA
The comparison of several group means for a continuous outcome, when differences in means are what the research question asks about and the variance handling can be justified.
BEFORE YOU RUN IT
Planning the Follow-Up Before the Omnibus Result
The comparisons you need are fixed before the omnibus test is run, because a follow-up chosen after seeing the output is hard to defend and hard to adjust correctly.
Unrelated Groups Only Each case is in one of three or more groups and is measured once. Repeated measures on the same participants need a rank test for related samples, and nested participants need a clustered model.
Which Pairs Matter List the comparisons that answer the research question, all pairs or only those against a control. Each extra comparison widens the adjustment, so a focused list keeps more power.
Shapes and Spread If the group distributions have similar shapes, a statement about medians becomes possible. With different shapes the test addresses whether values tend to be larger in some groups, and the wording follows.
Group Sizes and Ties Very unequal groups, a group with few cases or many tied values change how reliable the approximation is. Report the group sizes, and count ties when the outcome is a short rating scale.
IN SPSS
How to Run the Kruskal-Wallis Test in SPSS
The outline is for IBM SPSS. The Independent Samples dialog prints the pairwise table, while the legacy K Independent Samples dialog prints the omnibus test only, so labels and follow-up differ by version.
- Confirm the design: one ordinal or continuous outcome and one factor with three or more independent groups.
- Plot the outcome by group and compare shapes, spreads and group sizes.
- Open Analyze, Nonparametric Tests, Independent Samples (Legacy Dialogs, K Independent Samples in the older layout), and assign the outcome and the grouping variable.
- Under Settings, choose the Kruskal-Wallis test for k samples and set multiple comparisons to all pairwise.
- Run it and read the omnibus summary first, then the pairwise table.
- Compute the effect size from H and N, and plot the groups for the write-up.
READING THE OUTPUT
Reading the Omnibus Summary and the Pairwise Table
Kruskal-Wallis pairwise comparisons in SPSS appear in a table of their own with two significance columns, and the unadjusted one is the column most often quoted by mistake.
| Output element | What it tells you | What to check |
|---|---|---|
| Hypothesis Test Summary | The null hypothesis that the outcome has the same distribution across groups, and the decision | That the decision line is not reported as the result |
| Independent-Samples Kruskal-Wallis Test Summary | Total N, the statistic H, its degrees of freedom and the asymptotic significance | That H is reported with df and N, and that the legacy row labeled Kruskal-Wallis H (Chi-Square in older versions) is the same statistic |
| Ranks (legacy dialog) | The N and mean rank of each group | That mean ranks are not described as medians |
| Pairwise Comparisons | Each pair of groups with the test statistic, standard error, Sig. and Adj. Sig. | That Adj. Sig. is reported and the adjustment named in the footnote is stated in the text |
| Footnote on the adjustment | The method used to adjust significance across all pairs (Bonferroni in the default output) | That the family of comparisons matches the number of pairs examined |
| Pairwise comparison diagram (recent layouts) | The mean rank of each group with links marking the pairs that differ | That it is used as a visual summary, since it shows no intervals |
| Exact significance (where requested) | The p-value without the chi-square approximation to H | That small groups are checked with it where your license offers the option |
REPORTING
Reporting H, the Follow-Up and an Effect Size
The blanks come from the omnibus table, the pairwise table and your own effect size calculation, and none of them is a result.
Write the omnibus result as H(df) = ___, N = ___, p = ___, then name the pairwise method and the family of comparisons it adjusts over. Report the adjusted significance for each pair that answers the research question, and describe the direction in words from the mean ranks or the group distributions. SPSS prints no effect size for this test, so add an epsilon squared effect size computed from H and N, with any interval taken from a bootstrap or another program. Give the group sizes and a summary of each group, such as the median with the interquartile range, plus a plot. State a difference in medians only when the group shapes were similar.
COMMON MISTAKES
Six Slips After a Significant Omnibus Result
Reviewer questions cluster after the omnibus test, and four of these six concern the follow-up and the effect size.
Unadjusted p Quoted The Sig. column of the pairwise table ignores the number of comparisons. The adjusted column is the one to report, with the adjustment method named in the text.
No Follow-Up at All A significant H says that not all groups are alike and nothing more. Without adjusted pairwise results the reader cannot tell which groups differ or in what direction.
Pairs Chosen After the Fact Running all pairs and keeping the significant ones turns a scan into a result. A list of prespecified comparisons, or a clear exploratory label, keeps the interpretation honest.
H Without an Effect Size A small p-value in a large sample can describe a trivial difference. An epsilon squared with an interval, or a pairwise effect size, shows how much the groups differ.
Medians Read Into the Result Differences in group medians are reported as what the test found. That needs similar distribution shapes. Otherwise the test describes a tendency for values to be larger, and the wording follows.
Related Measures as Groups Three conditions measured on the same participants are not independent groups. A rank test for related samples matches that design, and treating the columns as groups ignores the pairing.
Already run this analysis? Independent Statistical Review checks the omnibus test, the adjustment of the pairwise comparisons and the effect size before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About the Kruskal-Wallis Tables
Two significance columns, the missing effect size and an omnibus result with no significant pair are the questions this output raises, along with planning the follow-up comparisons.
Why does the pairwise table in SPSS show two significance columns?
Sig. is the unadjusted p-value of each pair, and Adj. Sig. is the value adjusted for the number of comparisons, which is the one to report. The default adjustment is Bonferroni, and the footnote under the table names it. It is conservative when there are many groups, so a short list of planned comparisons costs less power than all pairs.
Does SPSS give an effect size for the Kruskal-Wallis test?
Not in the standard output. A common choice is epsilon squared, computed from the H statistic and the total N, and another is eta squared based on H. Either is accompanied by an interval from a bootstrap or another program, and the text names which one was used so that the figure can be reproduced.
Why is the overall test significant when no single pair is?
The omnibus test and the adjusted pairwise tests answer different questions and are adjusted differently, so they can disagree. The overall test can detect a pattern spread across all groups, while each pair has to clear an adjusted threshold alone. Report both as they are, and do not search for another adjustment until a pair passes.
Can a statistician plan the follow-up comparisons for my groups?
Yes. An in-house PhD-level statistician can confirm which comparisons answer your research question, review the adjustment and the effect size in your output, or carry out the analysis on your data. For the tables and the write-up alone, Results Reporting & Interpretation covers that stage. The interpretation and the conclusions remain yours.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
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