METHOD GUIDE
Mann-Whitney U Test in SPSS
What It Compares and When Exact Significance Matters
A significant U does not by itself show that two medians differ, and SPSS offers two dialogs that print different tables. Here are the design checks, the two kinds of significance value, and an effect size to report beside them.
IN SHORT
What the Test Compares and What to Report With It
A Mann-Whitney U test compares two independent groups through the ranks of an ordinal or continuous outcome, and asks whether values in one group tend to be larger than values in the other. It supports a statement about medians only when the two distributions have the same shape. To run the Mann-Whitney U test in SPSS, open Analyze, Nonparametric Tests, Independent Samples (Legacy Dialogs, 2 Independent Samples in the older layout), define the two groups, and request exact significance when groups are small or tied values are common. 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
A rank-sum result answers a narrower question than most write-ups imply. Where the gap between two means is what the study needs, the t-test beside the rank comparison is the better-suited analysis.
Mann-Whitney U Test
The rank-based comparison of two independent groups carried out within your study design, with the shape check, the effect size with an interval and the reporting agreed for your data.
Independent Samples t-Test
A comparison of two independent group means for a continuous outcome, when the difference in means is the quantity of interest and its precision is needed.
BEFORE YOU RUN IT
Choices Behind a Defensible Rank Comparison
Four choices decide what a significant U can be taken to mean, and they are cleaner when settled from the design and the outcome scale before any table is read.
Two Unrelated Groups Each case sits in one group and is measured once. Matched pairs, repeated visits or participants clustered in clinics break independence and call for a paired test or a model for clustered data.
What You Want to Compare Ranks answer whether one group tends to score higher. If the question is about medians or means, say which, because the test supports a statement about medians only when the shapes match.
Shape in Each Group Plot both distributions side by side. Similar shapes allow a location-shift reading, while one skewed and one symmetric group mean the result describes a tendency to score higher, not a median gap.
Ties and Group Size Many tied values, common on rating scales, and very small groups weaken the normal approximation. Exact significance is the safer basis there, where your SPSS version and license provide it.
IN SPSS
How to Run the Mann-Whitney U Test in SPSS
The outline is for IBM SPSS. The SPSS independent samples nonparametric test dialog prints a test summary with a distribution plot, the legacy dialog prints rank and test statistics tables, and labels differ by version.
- Confirm the design: one ordinal or continuous outcome, two independent groups, each case counted once.
- Plot the outcome in each group and compare the shapes, not only the centers.
- Open Analyze, Nonparametric Tests, Independent Samples (Legacy Dialogs, 2 Independent Samples in the older layout), and assign the outcome and the grouping variable.
- Choose the Mann-Whitney U test, and request exact significance where your version and license offer it.
- Run it and read the group sizes and rank summaries before the test statistic.
- Compute an effect size from the output or in another program, and keep the plot for the write-up.
READING THE OUTPUT
Asymptotic or Exact: Reading the Two Layouts of the Output
The same test appears in two layouts, and the most misread element is which of two significance values, asymptotic or exact, belongs in the write-up.
| Output element | What it tells you | What to check |
|---|---|---|
| Hypothesis Test Summary | The null hypothesis, the test used and the decision at the default .05 | That the decision line is not quoted in place of the statistic and the p-value |
| Ranks (legacy dialog) | The N, mean rank and sum of ranks of each group | That the group with the higher mean rank is named in the sentence, as no direction is printed |
| Mann-Whitney U and Wilcoxon W | The U statistic and the sum of ranks of the smaller group | That U is reported with both group sizes, since its range depends on their product |
| Z (Standardized Test Statistic) | The normal approximation of U, corrected for ties | That it is quoted only where the approximation is justified by group size |
| Asymp. Sig. (2-tailed) (Asymptotic Sig. (2-sided test) in the Independent Samples dialog) | The p-value from the normal approximation | That it is checked against the exact value when groups are small or ties are frequent |
| Exact Sig. (where printed or requested) | The p-value from the exact distribution of U | That the text says which version was reported, and that tie handling matches your data |
| Distribution plot (recent layouts) | Histograms of the outcome by group with mean ranks | That shapes are compared before any statement is made about medians |
REPORTING
What to Report Beside U and p
A frame with placeholders only: each number comes from your output, and nothing in it is a result.
Write U = ___, the group sizes n1 = ___ and n2 = ___, and the p-value, saying whether it is exact or asymptotic. Add an effect size with a direct reading, the probability that a randomly chosen case from the group with the higher mean rank scores higher than one from the other group, with ties counted as half. It is U divided by the product of the two group sizes, or 1 minus that value, whichever is larger, because the printed U is not always counted for the higher group. In most versions the output prints no effect size or interval for this test, so an interval comes from a bootstrap or another program. Describe each group with a distribution summary such as the median and interquartile range, and a plot, and say in words which group tended to score higher. Mention medians in the conclusion only when the shapes were similar.
COMMON MISTAKES
Six Misreadings of a Rank-Sum Result
Six readings draw most queries on this test, and the first three come from treating a statement about ranks as one about medians.
Medians Assumed A significant U is reported as a difference in medians. That holds only for distributions of the same shape, and equal medians can still give a small p-value when the spreads differ.
Shapes Never Compared Two histograms in one plot show whether a shift, a difference in spread or in skew drives the result, so the plot belongs in the analysis before the sentence about the result is written.
Asymptotic p With Few Cases With very small groups or many tied values the normal approximation can be inaccurate. Exact significance is then the value to report, and the text states which version was used.
U Without Context U alone does not say which group is higher or by how much. Group sizes, a distribution summary and an effect size make the result readable by someone who has not seen the output.
Dependence Overlooked Siblings, classes or repeated visits make observations related while the test treats them as unrelated. The design shows this, and a paired test or a clustered model is the match.
Chosen After a t-Test Failed Switching to ranks because a t-test gave a larger p-value is a choice made after seeing the data. The test follows from the outcome scale and the question, and the decision is stated.
Already run this analysis? Independent Statistical Review checks the test choice, the p-value you reported and the wording of the conclusion before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About the Rank Output
W printed beside U, the choice between exact and asymptotic values and the meaning of mean ranks open the questions on this test.
Why does the output show a Wilcoxon W as well as the Mann-Whitney U?
They are two forms of the same rank-sum test, so both give the same p-value. W is the sum of ranks of the smaller group, and U is derived from it. Report U with the two group sizes, and mention W only if a journal asks for it. A paper that cites Wilcoxon’s version of the test describes the same comparison.
Which Mann-Whitney exact significance value should I report?
Report the exact significance when groups are small or tied values are frequent, and say that you did. The legacy dialog can print an Exact Sig. row, which is not corrected for ties, so with many ties the Exact option is the better route where your license includes it. With larger groups the asymptotic value is usually close, and the choice rarely changes the conclusion.
What do the mean ranks in the Ranks table mean?
A higher mean rank means that the group’s values tend to be larger once all cases are ranked together. Mean ranks come from the pooled ranking, so they depend on both group sizes and are not medians. Use them to say which group tended to score higher, and report medians and quartiles separately.
Can a statistician check the effect size and wording of my rank-based result?
Yes. An in-house PhD-level statistician can review your output and confirm the p-value version, the effect size and the wording of the conclusion, or carry out the comparison on your data with the shape check. For the tables and the write-up alone, Results Reporting & Interpretation covers that stage. The interpretation and the conclusions remain yours.
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Describe the outcome, the two groups and the output so far. Whether ranks suit your question, and what the write-up may claim from them, is settled with you during the assessment.
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