If your data did not meet the assumptions for a t-test, you probably ran a nonparametric test instead — and then discovered a second problem: how do you actually write the result up in APA style? The Mann-Whitney U test and the Wilcoxon signed-rank test are the two nonparametric tests students use most often, and they are also the two most commonly misreported. This guide shows you exactly what to report for each test, gives you copy-ready APA templates, and walks through a worked example for each one so you can adapt it to your own results.
Mann-Whitney U or Wilcoxon? Start Here
These two tests look similar, but they answer different questions, and mixing them up is the most common mistake of all.
Use the Mann-Whitney U test when you have two independent groups — for example, a treatment group and a control group, or men and women — and you want to compare their scores. It is the nonparametric alternative to the independent-samples t-test.
Use the Wilcoxon signed-rank test when you have two related measurements — for example, the same people measured before and after an intervention, or matched pairs — and you want to compare them. It is the nonparametric alternative to the paired-samples t-test.
A quick memory aid: independent groups mean Mann-Whitney; paired or repeated measurements mean Wilcoxon signed-rank. Note that the Wilcoxon rank-sum test is simply another name for the Mann-Whitney U test, so if your software output says “Wilcoxon rank-sum,” you are reporting a Mann-Whitney result, not a signed-rank result.
Reporting Mann-Whitney U Results in APA Style
What to report
For a Mann-Whitney U test, APA style expects four pieces of information, plus the medians that help the reader understand the direction of the difference:
- The median (Mdn) for each group.
- The U statistic.
- The z value (the normal approximation, reported by most software when samples are not tiny).
- The exact p value, and an effect size.
Report medians rather than means, because the Mann-Whitney test works with ranks, not raw means. If the two distributions have a roughly similar shape, you can describe the result as a difference in medians; if their shapes differ a lot, describe it more carefully as a difference in mean ranks or in the overall distribution of scores.
APA template
Use this sentence structure and fill in your own numbers:
Participants in the [Group A] group (Mdn = [value]) scored higher than those in the [Group B] group (Mdn = [value]), U = [value], z = [value], p = [value], r = [value].
Worked example
Imagine a study comparing anxiety scores (on a 0–60 scale) between students who attended a four-week mindfulness workshop (n = 28) and students on a waitlist (n = 30). The scores were skewed, so the researcher used a Mann-Whitney U test. This is an illustrative example, not data from a real study.
Students who attended the workshop (Mdn = 35) reported lower anxiety than students on the waitlist (Mdn = 42), U = 289, z = -2.14, p = .032, r = .28.
How to read this sentence: the negative z value simply reflects the direction of the ranking, and the p value of .032 means the difference would be unlikely if there were truly no difference between the groups. The effect size r = .28 is a medium effect by the usual rough benchmarks (around .10 is small, .30 is medium, and .50 is large). You can calculate r yourself with the formula r = z divided by the square root of the total sample size. Here, 2.14 divided by the square root of 58 gives .28.
In a results table
If you are reporting several tests, a table keeps things tidy. Include one row per comparison, with columns for the two groups, their sample sizes and medians, U, z, p, and r. Always give the medians alongside the test statistics — a U value on its own tells the reader nothing about which group scored higher.
Reporting Wilcoxon Signed-Rank Results in APA Style
What to report
For a Wilcoxon signed-rank test, APA style expects:
- The median (Mdn) at each time point or for each condition.
- The z value (the normal approximation reported by most software).
- The exact p value, and an effect size.
Some software also prints a W or T statistic. APA does not require you to report it if you report z and p, but if your supervisor or journal prefers it, you can add it: for example, “W = 62, z = -3.02, p = .003.” Check your institution’s preference and stay consistent across your thesis.
APA template
Scores [after the intervention / in Condition B] (Mdn = [value]) were significantly [higher/lower] than scores [before the intervention / in Condition A] (Mdn = [value]), z = [value], p = [value], r = [value].
Worked example
Imagine 24 students completed an anxiety questionnaire before and after a four-week mindfulness workshop. Again, this is an illustrative example, not real data. The differences between before and after scores were not normally distributed, so the researcher used a Wilcoxon signed-rank test.
Anxiety scores after the workshop (Mdn = 14) were significantly lower than anxiety scores before the workshop (Mdn = 18), z = -3.02, p = .003, r = .62.
For the Wilcoxon test, calculate r by dividing z by the square root of the number of pairs: 3.02 divided by the square root of 24 gives .62, a large effect. Always state which version of the effect-size formula you used if your supervisor asks, because different textbooks divide by slightly different totals — what matters most is that your reader can follow your calculation.
Mann-Whitney U vs Wilcoxon Signed-Rank at a Glance
| Feature | Mann-Whitney U test | Wilcoxon signed-rank test |
|---|---|---|
| Design | Two independent groups | Two related measurements (paired or repeated) |
| Nonparametric alternative to | Independent-samples t-test | Paired-samples t-test |
| What it compares | Ranks of scores across two groups | Ranks of the differences within each pair |
| Report the median for | Each group | Each time point or condition |
| Key statistics | U, z, p, r | z, p, r (W or T optional) |
| Effect size formula | r = z / square root of total N | r = z / square root of number of pairs |
Common Mistakes to Avoid
- Reporting means instead of medians. The tests compare ranks, so means can mislead. Report medians as your descriptive statistics.
- Reporting U without z, p, and an effect size. A U value alone cannot be interpreted, and a p value alone says nothing about how big the difference is.
- Writing p = .000. Software prints .000 when the p value is very small, but a p value is never exactly zero. Write p < .001 instead.
- Using the Wilcoxon signed-rank test for independent groups, or the Mann-Whitney test for paired data. Check your design before you check your output.
- Reporting the wrong Wilcoxon. If your output says “Wilcoxon rank-sum,” that is the Mann-Whitney test, not the signed-rank test. Label it correctly in your write-up.
- Forgetting the direction of the difference. Always say which group or time point scored higher, using the medians to show it. A significant p value without a direction is only half a result.
- Copying every number from the output. Your reader needs U (or W), z, p, r, and the medians — not the mean ranks, sum of ranks, and asymptotic significance columns all pasted in.
Before You Submit: A Quick Checklist
- Have you named the correct test for your design?
- Have you reported medians for each group or time point?
- Have you included U (for Mann-Whitney) or z, the exact p value, and an effect size?
- Have you written p < .001 instead of p = .000 where needed?
- Have you stated the direction of the difference in plain words?
- Have you used the same format for every nonparametric test in your results section?
If you can tick all six boxes, your nonparametric results are ready for your supervisor, your examiner, or a journal reviewer.
Frequently Asked Questions
Do I report U or z for the Mann-Whitney test?
Report both: U = [value], z = [value], p = [value]. The U value identifies the test statistic, while z is the standardised value most readers use to judge the result and to compute the effect size.
What if my software only gives me U and p, with no z?
You can still report U and p, and you can compute an effect size from the p value or from the rank-biserial correlation if your software offers it. If you can, ask your software for the normal approximation (in SPSS, this appears with larger samples) so you can report z as well.
Should I report means or medians with nonparametric tests?
Report medians. These tests are based on ranks, and medians describe the centre of skewed data far better than means. If you want to give means as extra information, label them clearly as supplementary descriptives, not as the basis of the test.
How do I report a non-significant Mann-Whitney or Wilcoxon result?
Use exactly the same format, but say so plainly. For example: “There was no significant difference between the two groups (Mdn = 32 vs. Mdn = 34), U = 402, z = -0.45, p = .652, r = .06.” Non-significant results are still results — report them fully, never hide them.