Reporting a Kruskal-Wallis Test in SPSS
H and Its Adjusted Follow-Ups
Reporting a Kruskal-Wallis test in SPSS joins two outputs, the omnibus H and the pairwise rows, into one account. The adjustment behind the pairwise p-values is named, and the effect size is labeled so a reader knows how it was obtained.
IN SHORT
How an Omnibus and a Pairwise Result Fit Together
A Kruskal-Wallis report states whether three or more independent groups differ in the distribution of an ordinal or continuous outcome, then which pairs differ once the number of comparisons is allowed for, and how large the difference is. For reporting a Kruskal-Wallis test in SPSS, H, df and p come from the output of Analyze, Nonparametric Tests, Independent Samples (or the Test Statistics table of Legacy Dialogs, K Independent Samples), and the pairs from the Pairwise Comparisons view of the newer output. Labels vary by release. Setting such a paragraph beside its saved output is part of the work of the in-house PhD-level statisticians at OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research.
In This Guide
ANALYSIS SUPPORT
Analysis Support for This Method
Which test fits several groups on an ordinal or skewed outcome shapes everything written afterwards. A comparison of means stays available when the outcome is continuous and the group distributions allow it.
Kruskal-Wallis Test
The rank-based comparison of three or more independent groups, carried out for your design, with follow-up comparisons and wording that fit the output.
One-Way ANOVA
The comparison of group means for a continuous outcome, with its assumptions judged in context and an effect size reported with its interval.
BEFORE YOU REPORT IT
What Is Settled Before H Is Quoted
A few points fix the shape of the paragraph, and they are easier to settle before copying than to repair in a revision.
Which Adjustment The pairwise table prints an unadjusted and an adjusted significance. The adjusted column is the one quoted, and the method named in the output note is the one written in the text.
Planned or Followed Up Pairs examined after a significant H are follow-ups. Pairs reported after a nonsignificant H are exploratory, and the paragraph labels them that way.
Which Effect Size H arrives without an effect size. Epsilon-squared or an eta-squared based on H can be computed from it, they can differ noticeably in small samples, and the paragraph names the one chosen.
What Medians Describe H tests the whole rank distribution. Medians per group describe each group, and read as the quantity tested they presume that the group shapes match.
IN SPSS
Which Value to Take From Which Output
The setup of the test, including how the pairwise view is opened, is covered in Kruskal-Wallis Test in SPSS: Checks and Output, and the values below are read from output that IBM SPSS has already produced.
Take H, df, N and the p-Value
From the test summary, or the Test Statistics table in the legacy layout, take the Test Statistic (H), Degrees of Freedom, the total N and the Asymptotic Significance.
Check: The df is the number of groups minus one. A df that disagrees with the group count suggests an empty or merged category in the grouping variable.
Take the Pairwise Rows
From the Pairwise Comparisons table, take for each Sample 1-Sample 2 pair the test statistic, the standard error and the adjusted significance.
Watch: Take the column labeled Adj. Sig., not Sig. The unadjusted value sits beside it and looks smaller, but only the adjusted one allows for the number of pairs examined.
Read Off the Adjustment Method
Find the adjustment named in the note under the pairwise table, and write that name into the results sentence.
Check: If a different method was selected in the dialog than the one you remember, the name comes from the output note, which records what was actually applied.
Take Medians for the Table
Run descriptive statistics split by group and take each group’s n, median and first and third quartiles.
Tip: List the groups in the order of the research question rather than alphabetically, so that the pairwise sentences can be followed down the table without searching.
Compute the Effect Size from H
Calculate epsilon-squared, or an eta-squared based on H, from the printed H, the total N and the number of groups.
Watch: SPSS prints neither in most versions. Label the value in the text, for example epsilon-squared (from H), so it is not confused with the eta squared of an ANOVA.
Compare Sentence and Pairwise Rows
Write the omnibus sentence first and the pairwise sentence after it, then compare both with the output tables.
Check: Count the pairs. Four groups give six, and the paragraph either reports all six or says which were reported and why the others were left out.
READING THE OUTPUT
From the Omnibus Test to the Pairwise Rows
The table runs through the printed elements in the order a results paragraph uses them, from the omnibus line to the follow-up rows.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| Test Statistic (Kruskal-Wallis H) | Test summary or Test Statistics table | H in the first sentence, written with its df and, in many styles, the N beside it |
| Degrees of Freedom | Same place | The df beside H, equal to the number of groups minus one, which also confirms the group count |
| Total N | Test summary | The N in the sentence, below the sample recruited if the outcome has gaps or a group code is missing |
| Asymptotic Sig. (2-sided test), or Asymp. Sig. in the legacy Test Statistics table | Same place | The omnibus p, with a printed .000 given as p < .001 and the exact value kept otherwise |
| Sample 1-Sample 2 | Pairwise Comparisons table | The pair, named by its group labels in the sentence, never by the numeric codes |
| Sig. | Pairwise Comparisons table | Unadjusted; left out of the text when an adjustment applies, since it reads smaller than the adjusted value |
| Adj. Sig. | Pairwise Comparisons table | The pairwise p, with the method of adjustment named once in the paragraph |
| Mean ranks and medians | Ranks table and a descriptive run | Ranks give the ordering the test used; medians go in the group table as description of each group |
REPORTING
One Paragraph and One Table for H and Its Pairs
The sentence carries the omnibus result and the pairs, while the table holds the group summaries that both refer to.
In Kruskal-Wallis APA format, the sentence gives H with its df and p, an effect size with its label, and pairwise results that name the adjustment. Reporting the H statistic with N is optional in some styles but useful here, because the N shows how many complete cases entered. The frame is for three groups.
A Kruskal-Wallis test, chosen because [reason], showed that [outcome] [differed / did not differ] across [Group A], [Group B] and [Group C], H(___) = ___, p = ___, ε² = ___ (from H). Pairwise comparisons with a [adjustment method] adjustment showed that [Group A] differed from [Group B] (adjusted p = ___) but not from [Group C] (adjusted p = ___). The adjustment covered all ___ pairs examined. Group medians and interquartile ranges are in Table 1.
| Table 1. Distribution of [Outcome] by [Group], With Kruskal-Wallis Results | ||||
|---|---|---|---|---|
| Group | n | Mdn | IQR (Q1 to Q3) | Mean rank |
| [Group A] | ___ | ___ | ___ to ___ | ___ |
| [Group B] | ___ | ___ | ___ to ___ | ___ |
| [Group C] | ___ | ___ | ___ to ___ | ___ |
| Note. H(___, N = ___) = ___, p = ___, ε² = ___ (from H). Pairwise p-values are adjusted by the [method]. Mdn = median; IQR = interquartile range. | ||||
Epsilon-squared, computed from H and the total N, runs from 0 to 1 and describes how much of the variation in ranks goes with group membership. An eta-squared based on H can fall below zero when H is smaller than the number of groups minus one, and in small samples the two can differ noticeably, so the paper names the one used and how it was derived. SPSS prints neither in most versions, and no interval comes with them, so an interval is obtained elsewhere, and benchmarks borrowed from ANOVA effect sizes are rough guides rather than thresholds. The inputs, H, the total N and the number of groups, are stated so that a reader can recompute the value.
COMMON MISTAKES
Kruskal-Wallis Paragraphs Read Against the Output
Each of these appears when the output is read in pieces, and each disappears once the paragraph is checked against the pairwise table as a whole.
Unadjusted p Quoted Taking the Sig. column in place of Adj. Sig. reports pairs as clearer than they are, since the number of comparisons has not been allowed for.
Adjustment Unnamed Saying only that pairwise comparisons were adjusted leaves the reader unable to reproduce them. The method printed in the output note is written out.
H Without Its df H cannot be read without its degrees of freedom, because the same value means different things for three groups and for six. The df stands inside the parentheses.
Significant Pairs Only Reporting only the pairs that reached significance hides how many were examined. The paragraph gives every pair or states how the reported ones were chosen.
Effect Size Without a Name A value printed with no label leaves the reader guessing between epsilon-squared and an eta-squared based on H, which can differ in small samples.
Medians Taken as the Test A table of medians read as what H compares promises more than the test gives. H addresses the rank distributions, and medians describe the groups.
Omnibus and pairwise rows both written up? Independent Statistical Review traces each figure in the paragraph to the output it came from, including the adjustment named.
FREQUENTLY ASKED QUESTIONS
Pairs, Labels and Medians After a Significant H
Pairwise statistics, effect size labels and tables of medians raise the same few doubts, and each is answered here against what the output prints.
Should the standardized statistic be reported for every pair?
Report the adjusted p-value for each pair, and add the standardized test statistic only where a journal or style guide asks for it. If it is given, it is given for every pair and not for a selection, and the adjustment is named once. The standard error and the unadjusted Sig. need not appear in the text.
Should epsilon-squared or eta-squared go in the paper?
Either is acceptable when it is labeled and computed from H. In small samples the two can differ noticeably, and an eta-squared based on H can fall below zero, so the label matters as much as the choice. If a target journal or a field’s convention prefers one, follow it, and give the total N and the number of groups so a reader can recompute it.
Do I report mean ranks or medians for each group?
Medians with quartiles describe the groups, and mean ranks show the ordering the test used. The group table can hold both. The text claims a difference in medians only when the group shapes are similar, and otherwise says that one group tended to have larger values in the sample.
What does it take to have an omnibus and pairwise write-up reviewed?
The saved output and the draft paragraph are enough for an in-house PhD-level statistician at OnlineSPSS to match H, the pairwise rows, the adjustment and the effect size line by line. This stage sits within Results Reporting & Interpretation, and the conclusions drawn from the groups remain with you.
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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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NEXT STEP
Do the Pairwise Rows Match
Your Text?
Omnibus H and the adjusted pairwise p-values are printed, while the effect size rests on H and the total N, so every figure in the paragraph has a source that can be checked.
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