How to Interpret Mann-Whitney U Test Output in SPSS (and Report It in APA 7)

The Mann-Whitney U test compares two independent groups when the outcome is ordinal or too skewed for a t-test. SPSS's output is short, two tables, but it prints two test statistics with different names, gives mean ranks instead of medians, and leaves the effect size for you to compute. This guide reads both tables row by row with a worked example, covers the newer Nonparametric Tests output, lists the misreadings, and gives the APA 7 write-up. The reporting format alone is in the Mann-Whitney U APA guide.

What SPSS gives you

Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples, with Mann-Whitney U ticked, produces:

1. Ranks: N, mean rank and sum of ranks for each group.
2. Test Statistics: Mann-Whitney U, Wilcoxon W, Z and the p value.

Analyze > Nonparametric Tests > Independent Samples (the newer procedure) gives the same test in a different layout; see the section on it below.

Neither procedure prints the medians you report. Get them from Analyze > Descriptive Statistics > Explore with the grouping variable as Factor.

The worked example

Forty patients were randomly assigned to a new or the standard version of a minor procedure, 20 per group, and rated their pain the next day on a 0 to 10 scale. Pain ratings are ordinal and bunch up at a few values, so a Mann-Whitney U test was used. All numbers below come from one dataset.

From Explore: new procedure Mdn = 3.5 (IQR 3 to 4); standard procedure Mdn = 5.0 (IQR 4 to 6).

Table 1: Ranks

SPSS ranks all 40 ratings together from lowest (rank 1) to highest (rank 40), giving tied ratings the average of their ranks, then adds the ranks up by group.

• N: 20 per group.
• Mean Rank: 15.50 for the new procedure, 25.50 for the standard one. Lower ranks mean lower pain, so the new-procedure group tended to report less pain. This is how you read the direction.
• Sum of Ranks: 310 and 510. They always add up to N(N + 1)/2 = 820.

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

The footnote reads "Grouping Variable: Procedure".

• Mann-Whitney U = 100.000: the test statistic you report. It counts, over all 400 possible pairs of one patient from each group, how often the new-procedure patient had the higher rating (ties count half). With no difference between groups, U would be near half of 400, 200. There are two possible U values, one counted from each group; here SPSS shows the smaller, and the other is 400 − 100 = 300.
• Wilcoxon W = 310.000: a rank sum, here the new-procedure group's (the group with the smaller mean rank), and U = W − 20 × 21 / 2 = 100. It is the same test expressed differently. Do not report it as a separate result.
• Z = −2.762: U converted to a standard normal score, corrected for ties. The sign only reflects which U SPSS used; read direction from the mean ranks.
• Asymp. Sig. (2-tailed) = .006: the two-sided p value from the normal approximation. This is the p you report.

For small samples the legacy table can add an Exact Sig. [2(1-tailed Sig.)]* row, footnoted "Not corrected for ties". With small groups and few ties, the exact p is the better choice; say which you report.

The effect size SPSS does not print

Compute r from Z and the total sample size: r = |Z| / √N = 2.762 / √40 = .44. By common benchmarks (.10 small, .30 medium, .50 large), that is a medium-to-large effect.

The newer Nonparametric Tests output

The Independent Samples procedure (not Legacy Dialogs) starts with a Hypothesis Test Summary that states the null hypothesis, names the test, gives Sig. and says "Reject the null hypothesis" or "Retain the null hypothesis". Its detail view (in recent versions printed directly, in older ones by double-clicking the summary) has an Independent-Samples Mann-Whitney U Test Summary with Total N, Mann-Whitney U, Wilcoxon W, Test Statistic, Standard Error, Standardized Test Statistic and Asymptotic Sig. (2-sided test).

• Standardized Test Statistic is the Z you use for r.
• The U it shows can be the other of the two U values (here it could read 300 instead of 100), so the sign of the standardized statistic can flip too. Both describe the same test: the two U values always add up to n1 × n2, and |Z| and p are the same.
• "Reject the null hypothesis" is not a write-up. Report the statistics.

Misreadings that cost marks

• Reporting Wilcoxon W as the test statistic. For a Mann-Whitney test report U. (W is also the name of the statistic in the Wilcoxon signed-rank test, a different test for paired data.)
• Reporting mean ranks as if they were medians. Report medians (and IQRs) from Explore; use mean ranks only for direction.
• Reading direction from the sign of Z. It depends on which U SPSS picked. The mean ranks tell you which group was higher.
• Leaving out the effect size. SPSS does not print one, so compute r = |Z| / √N.
• Writing p = .000. Write p < .001.
• Saying the test compares medians. Strictly, it tests whether a value from one group tends to be larger than a value from the other. It compares medians only if the two distributions have the same shape.

The APA 7 format template

A Mann-Whitney U test showed that [dependent variable] was significantly lower/higher in [group 1] (Mdn = X.XX) than in [group 2] (Mdn = X.XX), U = X.XX, z = X.XX, p = .XXX, r = .XX.

The write-up for this example

A Mann-Whitney U test showed that pain ratings the day after the procedure were significantly lower with the new procedure (Mdn = 3.5, IQR 3–4) than with the standard procedure (Mdn = 5.0, IQR 4–6), U = 100.00, z = −2.76, p = .006, r = .44.

Some write-ups give the sample sizes inside the sentence ("ns = 20") or report the mean ranks as well (15.50 vs 25.50). Both are fine; the medians are what readers understand.

Let KyroStat do the write-up for you

Already have the output? Paste the Test Statistics table from the SPSS Viewer into the box on the Mann-Whitney U reporting guide to get the APA sentence. Or upload the spreadsheet to KyroStat, which picks the test from your data, computes the medians and the effect size r, and writes the APA 7 sentence and table with the code behind every number.

Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal

Frequently asked questions

Do I report Mann-Whitney U or Wilcoxon W? U. Wilcoxon W is the rank sum of one group and expresses the same test differently; it is not a second result.

How do I get the effect size for a Mann-Whitney test in SPSS? SPSS does not print it. Divide the absolute value of Z by the square root of the total N: r = |z| / √N.

What does mean rank mean? The average position of a group's scores when everyone's scores are ranked together. A higher mean rank means that group tended to score higher.

Should I report Asymp. Sig. or Exact Sig.? Asymp. Sig. for moderate and large samples. With small groups, the exact p is more accurate; name whichever you use.

Why does the newer Nonparametric Tests procedure show a different U? There are two U values, one counted from each group, and they always add up to n1 × n2. The two procedures can show different ones; |Z| and p are identical.

Which related guides might I need? Often these: independent-samples t-test output, the Wilcoxon signed-rank test for paired data and the Kruskal-Wallis test for three or more groups.