Two independent groups and an outcome that is ordinal, skewed, or shaped by outliers. What the test compares, why it is not simply a test of medians, and how to report it in APA 7.
The Mann-Whitney U test compares two independent groups by ranking every observation in the combined sample and asking whether the ranks are distributed differently between them. It is the rank-based counterpart to the independent-samples t test.
The cleanest way to describe what it estimates: pick one person at random from each group. Mann-Whitney asks whether the person from the first group is more likely to score higher than the person from the second. That framing is both accurate and easy for a reader to follow.
It is often called a test of medians. That holds only when the two distributions have similar shapes. Where the shapes differ, a significant U can reflect a difference in spread rather than a shift in the center, so describe the result as a tendency rather than asserting a median difference you have not tested.
The result opens with four figures: U labelled as the rank sum, z, p stated as two-tailed, and r as the effect size.
The two-tailed label is worth noticing. A one-tailed p on a rank test halves your apparent p value, and stating the direction on the result removes any ambiguity about which was reported.
The r effect size is the part most write-ups omit. U on its own is uninterpretable across studies because it scales with sample size; r does not. A comparison returning U = 3064.5, z = −0.56, p = .575, r = 0.04 is not merely non-significant, it is an effect of essentially zero magnitude, and reporting r says that plainly where p alone leaves it open.
Note that U is a large number even when nothing is happening. Do not read its size as evidence of anything.
Reach for it when the outcome is ordinal, when the distribution is clearly skewed, or when outliers would dominate a mean. It is also the right instinct for small samples where normality is unverifiable rather than merely unproven.
Do not reach for it automatically when a normality test flags at large n. The t test is robust to moderate departures, and with unequal variances the Welch correction handles the harder problem that Mann-Whitney does not address at all.
It is not a fix for unequal variances. This is a common misunderstanding. If the concern is different spread between groups, the Welch t test addresses it directly. Mann-Whitney assumes similar shapes if you want to read it as a median comparison, which makes it the wrong tool for that problem.
For two measurements on the same people, use the Wilcoxon signed-rank test. For three or more groups, use Kruskal-Wallis.
Lay the data out in long format: one row per person, one column holding the two-level group label, one column holding the outcome.
Open Nonparametric & Categorical and select Mann-Whitney U from the test list, then configure the variables in the Setup panel on the right. Results appear in the center.
Upload ordinal categories as text rather than numeric codes so the variable is typed as a category rather than a quantity.
Look at the distributions first. Descriptives and Explore will show whether the two groups have similar shapes, which is the condition that decides whether you may describe the result in terms of medians.
Use the action bar to add the result to a report, copy the table, or copy the APA text.
Report U, z, the two-tailed p, the effect size, and the group sizes. Give medians with an interquartile range rather than means.
A Mann-Whitney U test found no difference in job performance between the 25-34 and 35-44 age groups, U = 3064.5, z = −0.56, p = .575 (two-tailed), r = .04.
Include r. A non-significant p with an r of .04 is a much stronger statement than a p value alone, because it distinguishes no detectable effect from no effect worth detecting.
State which direction any difference runs. A U statistic tells a reader nothing about which group scored higher.
If you describe the finding as a median difference, say that you checked the distributions had similar shapes. If you did not check, describe it as a tendency.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's correlation and nonparametric procedures are validated against R's cor and against hand-computed closed-form values, matched exactly. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Nonparametric is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Independent-samples t test the parametric counterpart · Wilcoxon signed-rank for paired measurements · Kruskal-Wallis for three or more groups · the complete list on the analyses page.