Reporting a Mann-Whitney U Test in SPSS
Rank Results Without Median Claims
Reporting a Mann-Whitney U test in SPSS needs U, z and a p-value whose type is named, with the size and a distribution summary of each group. The sentence says which group tended to score higher and avoids calling a rank result a median gap.
IN SHORT
What a Rank-Sum Report Has to Contain
A Mann-Whitney report states which of two independent groups tended to have the larger values, and supports that with the test statistic, the type of p-value, both group sizes, a summary of each group’s distribution and an effect size. For reporting a Mann-Whitney U test in SPSS, the rank values come from the output of Analyze, Nonparametric Tests, Independent Samples, or from the Ranks and Test Statistics tables of the Legacy Dialogs route, while medians and quartiles come from a separate descriptive run. Menu and table labels differ between versions. At OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, rank-test paragraphs are set against the saved output by in-house PhD-level statisticians.
In This Guide
ANALYSIS SUPPORT
Analysis Support for This Method
A rank comparison answers a different question from a comparison of means, and the report follows whichever the design called for.
Mann-Whitney U Test
The comparison of two independent groups on ranks, carried out for your design, with the shape check and a result sentence that fits what ranks can show.
Independent Samples t-Test
The difference between two group means with its confidence interval, for a continuous outcome where the size of that difference is the question.
BEFORE YOU REPORT IT
What the Rank Result Can Be Said to Show
Four decisions are made before a number is copied, because each one changes what the paragraph is allowed to claim.
Exact or Asymptotic p Decide which p-value is quoted and name it in the text. The two can differ when groups are small or tied values are common, so the sentence cannot leave the type unsaid.
Ranks or Medians A significant U supports a statement that one group tended to have larger values. A statement about medians holds only when the two shapes match, so choose the claim first.
Which Group Sizes The test uses cases with a valid outcome and group code. Report n for each group, which is below the number recruited whenever the outcome has missing values.
Where Direction Comes From U and p show no direction. The mean ranks or the medians settle which group tended higher, and the sentence names the one it relies on.
IN SPSS
Which Value to Take From the Rank Output
Every value below is printed by IBM SPSS, and how the test was set up, including the exact option, is covered in Mann-Whitney U Test in SPSS: Checks and Output.
Take U, z and Both Group Sizes
From the test output, take the Mann-Whitney U, the Z (Standardized Test Statistic in the newer layout) and the number of cases in each group.
Check: Some layouts show only a total N beside the test. A separate Frequencies run on the grouping variable then gives n for each group, which the sentence needs.
Choose the p-Value to Report
Take the Asymp. Sig. (2-tailed), called Asymptotic Sig. (2-sided test) in the newer layout, or the Exact Sig. where it was requested.
Watch: A printed .000 means p < .001. Whichever type is taken, state it in the sentence, and keep one type throughout the paper unless the text explains why it changed.
Take Medians and Quartiles
Run descriptive statistics split by group, and take the median with the first and third quartiles of each.
Tip: Quartile definitions differ between programs, so give the interquartile range as the two quartile values rather than a single width, and the spread stays readable.
Compute the Effect Size by Hand
In most versions no effect size is printed, so compute r as z divided by the square root of the total N, or a rank-based correlation from the mean ranks.
Check: The N under the square root is the total number of observations in both groups, not the size of one group. The text states how the value was obtained.
Read the Direction From the Ranks
Take the mean ranks from the Ranks table, or the distribution summary of the newer layout, to see which group tended to have larger values.
Watch: Mean ranks come from the pooled ranking and are not medians. Use them for direction only, and keep the medians in the group table.
Check the Paragraph Against Ranks
Enter the values in the paragraph and the group table below, then set both against the saved output once more.
Check: The asymptotic p follows from z, so a pair that disagrees suggests values copied from two runs. An exact p can differ a little from the one z implies, which is expected.
READING THE OUTPUT
Where Each Value in the SPSS Rank Output Goes
This table follows the output from the statistic to the descriptive run and says what each value becomes in the paragraph or the group table.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| Mann-Whitney U | Test Statistics table, or the test summary | The statistic, reported with n for each group beside it, since U depends on both sizes |
| Wilcoxon W | Same table | Usually left out of the paper; it is the rank sum of one group, and it gives the same p-value as U |
| Z, or Standardized Test Statistic | Same table | The z in the sentence and the numerator of r; its sign may not show direction, so direction is taken from the ranks |
| Asymp. Sig. (2-tailed) | Same table | The asymptotic p from the normal approximation, with a printed .000 reported as p < .001 and the type named |
| Exact Sig. | Same table, where requested; older layouts may print Exact Sig. [2*(1-tailed Sig.)] for small samples unasked | The exact p, named as exact in the sentence; the older form is not corrected for ties, so say which was printed |
| N and Mean Rank | Ranks table | n for each group and which group tended higher; mean ranks come from the pooled ranking and are not medians |
| Median, first and third quartile | Separate descriptive run | The group table, one row per group, with the quartiles given as two values and not as a single width |
REPORTING
An APA 7 Paragraph With Group Medians and a Computed r
The paragraph and the group table repeat the same figures, so one source in the output stands behind each number.
In Mann-Whitney U APA format, the statistic is reported as U = ___ with z and a p-value of a named type, followed by the group sizes. Reporting medians for Mann-Whitney comparisons is description, so the sentence about the finding speaks of one group tending to have larger values. The frame below is for two independent groups.
A Mann-Whitney U test, chosen because [reason], compared [outcome] between [Group A] (n = ___) and [Group B] (n = ___). [Group A] tended to have [higher / lower] values (Mdn = ___, IQR = ___ to ___) than [Group B] (Mdn = ___, IQR = ___ to ___), U = ___, z = ___, [exact / asymptotic] p = ___, r = ___. The two distributions were [similar / different] in shape, so the result is stated as [a shift in the medians / a tendency for one group to score higher].
| Table 1. Distribution of [Outcome] by [Group], With Rank-Sum Test Results | ||||
|---|---|---|---|---|
| Group | n | Mdn | IQR (Q1 to Q3) | Mean rank |
| [Group A] | ___ | ___ | ___ to ___ | ___ |
| [Group B] | ___ | ___ | ___ to ___ | ___ |
| All cases | ___ | ___ | ___ to ___ | |
| Note. U = ___, z = ___, [exact / asymptotic] p = ___, r = ___ (z divided by the square root of N = ___). Mdn = median; IQR = interquartile range; mean rank is taken from the pooled ranking. | ||||
The effect size r is z divided by the square root of the total N, and it is read like a correlation, with the sign given in words. A rank-based correlation from the mean ranks, or the probability that a case from one group exceeds a case from the other, answers the same question on another scale, and the text names whichever is used. SPSS prints no interval for any of these in most versions, so an interval comes from another program, and without one the paper calls the value a point estimate. The value is computed from the printed z and N, so it can be reproduced from the saved output.
COMMON MISTAKES
Reporting Slips With a Rank-Sum Test
Laying the printed output beside the finished paragraph, one value at a time, brings each of these to light.
A Median Gap Claimed Stating that the medians differed because U was significant. The test compares rank distributions, and medians serve as description unless the two shapes match.
The p Type Left Unsaid A p-value with no word on exact or asymptotic cannot be traced to the output, and the two can differ when groups are small or tied values are common.
Only a Total N U depends on both group sizes, so a total alone leaves the reader unable to judge the result. Each group's n belongs in the sentence and the table.
r From the Wrong N An effect size computed from the size of one group, or from the sample recruited, does not match the z beside it. The total N of the test is the one used.
Higher Group Unnamed A sentence saying the groups differed, with no word on which tended higher, cannot be checked against the ranks. U and p carry no direction, so mean ranks or medians supply it.
Mean Ranks as Medians Mean ranks placed in a column headed median describe the pooled ranking, not the group. Medians come from the descriptive run and stand in their own column.
Unsure that U, z and r agree with each other? Independent Statistical Review compares each reported value with your saved output and the paragraph that carries it, line by line.
FREQUENTLY ASKED QUESTIONS
The Sign of z, the N for r and the Missing Interval
A negative z and the N behind r raise doubts first, and the fourth answer covers what can be reported from the rank output alone.
Why is z negative when the first group scored higher?
The sign of z reflects how SPSS forms the statistic, so it need not show which group was higher. Take the direction from the mean ranks or the medians and state it in words. Quote z as printed, or by its absolute value if the style guide asks for that, and use one convention for z and for r throughout.
Which N goes into the effect size r?
The total number of observations used by the test, which is the sum of the two group sizes. Cases without a valid outcome or group code drop out, so this N can be smaller than the sample recruited. Use the N the output prints for the test when it shows one, and report r with its direction in words and a note on how it was computed.
Can the effect size carry a confidence interval?
Yes, although SPSS prints no interval for it in most versions. An interval for r is calculated outside the SPSS output, in another program or by resampling the raw data. When none is given, the paper calls r a point estimate and leaves its precision unstated rather than implying it.
What can be prepared if I only have the rank output and no text yet?
A paragraph and a group table can be prepared from the saved output alone: U, z, the p-value type, n for each group and the direction read from the mean ranks. Medians and quartiles need a descriptive run, so the data file is needed for those. This work sits within Results Reporting & Interpretation, and the claim about the two groups stays with the author.
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