Your Shapiro-Wilk test returned p = .006, and now you cannot run an independent-samples t-test. The normality assumption is violated, the sample has only 22 participants per group, and your supervisor wants results by Friday. This is exactly the situation the Mann-Whitney U test was designed for. It compares two independent groups without requiring normally distributed data, and SPSS runs it in under a minute. Here is how it works, how to read the output, and how to report it in your thesis.
What the Mann-Whitney U Test Does
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares the distributions of two independent groups. Where the independent-samples t-test compares group means, the Mann-Whitney compares ranks. It answers a straightforward question: do values from one group tend to be higher or lower than values from the other?
The test makes no assumption about the shape of the distribution. It works with skewed data, ordinal scales (like Likert items), and small samples where normality cannot be verified. The only requirements are that the two groups are independent, the dependent variable is at least ordinal, and the observations within each group are independent of one another. In a typical project, a researcher might compare stress scores between 18 nursing students and 24 medical students after a Shapiro-Wilk test showed that stress scores in the nursing group were significantly non-normal (W = .87, p = .004).
How It Works: The Ranking Logic
The procedure is mechanical. First, all observations from both groups are pooled into a single list and sorted from smallest to largest. Each value receives a rank: the smallest gets rank 1, the next gets rank 2, and so on. Tied values receive the average of the ranks they would have occupied. If three observations share the same value at positions 5, 6, and 7, each gets a rank of 6.
Once ranked, the procedure separates the observations back into their original groups and sums the ranks within each group. These rank sums are the raw material. The U statistic is calculated from the rank sums and the group sizes. If the two groups come from the same distribution, you would expect their rank sums to be roughly proportional to their sample sizes. A large difference between the observed and expected rank sums produces a small U value. For samples larger than about 20, SPSS converts U to a z-score and calculates a p-value from the standard normal distribution. For smaller samples, it uses exact significance based on all possible permutations of the ranks.
Consider a concrete example. Suppose Group A (n = 15) has a mean rank of 19.8 and Group B (n = 15) has a mean rank of 11.2. The ranks cluster higher in Group A, which tells you that participants in Group A scored consistently above those in Group B. The U statistic quantifies exactly how much separation exists between those rank distributions.
When to Use Mann-Whitney (and When Not To)
The test fits three common situations. First, when the Shapiro-Wilk test rejects normality in one or both groups and your sample is too small for the Central Limit Theorem to rescue a t-test (roughly below 30 per group). Second, when the dependent variable is ordinal rather than continuous, such as satisfaction rated on a 5-point scale. Third, when the sample contains extreme outliers that would distort the mean but have little effect on ranks.
There is, however, a mistake that appears in roughly one of every five projects we review. A student runs the Shapiro-Wilk test, gets p = .12 (non-significant, meaning normality holds), and still runs the Mann-Whitney "just to be safe." This costs statistical power. The Mann-Whitney has about 95% of the power of a t-test under ideal conditions, meaning it needs a slightly larger sample to detect the same effect. With 30 participants per group, the t-test might detect a medium effect (d = .50) at 80% power, while the Mann-Whitney would need about 33 per group for the same detection rate. When your data actually are normal, the t-test is the better tool. Run the normality check first and let the result guide your choice. Our article on t-test versus ANOVA covers the parametric side of this decision in more detail.
Reading the SPSS Output
In SPSS, you run the test through Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples. Move your dependent variable into the Test Variable List, your grouping variable into the Grouping Variable box, define the two groups, check "Mann-Whitney U" under Test Type, and click OK.
SPSS produces two tables. The first, "Ranks," shows each group's sample size, mean rank, and sum of ranks. The mean ranks tell you which group scored higher. If Group A has a mean rank of 28.4 and Group B has a mean rank of 17.6, Group A's values are generally larger.
The second table, "Test Statistics," contains the numbers you need for your thesis. The Mann-Whitney U value is the test statistic itself. The Wilcoxon W is the smaller of the two rank sums (SPSS reports both). The z-value is the standardized version of U, used for samples above about 20. Asymp. Sig. (2-tailed) is your p-value. If this value falls below .05, the difference between groups is statistically significant. For small samples, check the "Exact Sig." row instead of the asymptotic one, since the exact test handles small-sample distributions more accurately. Academic Stats Agent produces all of these values automatically and formats them for APA reporting.
APA Reporting and Effect Size
A properly reported Mann-Whitney result in APA format looks like this: "A Mann-Whitney U test indicated that stress scores were significantly higher in the nursing group (Mdn = 34) than in the medical group (Mdn = 27), U = 234, z = -2.45, p = .014, r = .28." Note that you report medians, not means. Since the test works on ranks, the median is the appropriate measure of central tendency.
The effect size r is not provided by SPSS. You calculate it yourself using the formula r = z / √N, where z is the z-value from the output and N is the total number of observations across both groups. In the example above, with z = -2.45 and N = 42 + 34 = 76, the calculation is r = 2.45 / √76 = 2.45 / 8.72 = .28. Use the absolute value of z for this calculation. Cohen's benchmarks for r are .10 (small), .30 (medium), and .50 (large). An r of .28 falls just below medium, indicating a practically meaningful but moderate effect. For a deeper discussion of when and how to report effect sizes, see our effect size guide.
Mann-Whitney vs. Independent T-Test
The table below summarizes the key differences between the two tests so you can make the right choice quickly.
| Feature | Independent T-Test | Mann-Whitney U Test |
|---|---|---|
| What it compares | Group means | Group rank distributions |
| Normality assumption | Required (or large n) | Not required |
| Data level | Continuous (interval/ratio) | Ordinal or continuous |
| Central tendency reported | Mean (M) and SD | Median (Mdn) |
| Effect size | Cohen's d | r = z / √N |
| Statistical power (normal data) | Higher | ~95% of t-test power |
| Sensitivity to outliers | High | Low (uses ranks) |
| SPSS path | Analyze > Compare Means | Analyze > Nonparametric Tests |
The Paired Equivalent: Wilcoxon Signed-Rank Test
The Mann-Whitney handles independent groups. When the same participants are measured twice (pre-test and post-test, for example), you need the Wilcoxon signed-rank test instead. It is to the paired-samples t-test what the Mann-Whitney is to the independent-samples t-test.
The Wilcoxon signed-rank test calculates the difference between each participant's two scores, ranks the absolute values of those differences, and then compares the sums of positive and negative ranks. In SPSS, run it through Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples. APA reporting follows a similar pattern: "A Wilcoxon signed-rank test showed that post-intervention anxiety scores (Mdn = 22) were significantly lower than pre-intervention scores (Mdn = 31), T = 45, z = -3.12, p = .002, r = .44." The effect size formula is the same: r = z / √N, where N is the total number of pairs (not individual observations).
Key takeaway: Use the Mann-Whitney U test when Shapiro-Wilk rejects normality (p < .05) in at least one group and the sample is too small for the Central Limit Theorem to apply. Report medians, U, z, p, and r = z / √N with benchmarks of .10/.30/.50. Do not default to Mann-Whitney when normality holds; you lose statistical power for no reason. For paired designs with violated normality, switch to the Wilcoxon signed-rank test.
Frequently Asked Questions
Is the Mann-Whitney U test the same as the Wilcoxon test?
The Mann-Whitney U test is mathematically equivalent to the Wilcoxon rank-sum test; both compare two independent groups. It is not the same as the Wilcoxon signed-rank test, which is the paired-samples alternative used for repeated measurements on the same participants.
Can the Mann-Whitney U test handle tied values?
Yes. Statistical software applies a tie correction to the normal approximation, so the test remains valid with tied ranks. Many ties, common with Likert-type data, slightly reduce statistical power but do not invalidate the result.
Does the Mann-Whitney U test compare medians?
Only under a specific condition. The test compares the distributions of two groups; it can be interpreted as a comparison of medians only when both distributions have a similar shape. Otherwise it tests whether values in one group tend to be larger than in the other.