Table of Contents
The Mann-Whitney U test compares two independent groups on a non-normal, ordinal, or skewed outcome to see which group tends to score higher. Use it instead of an independent t-test whenever your data fail normality checks or exist only as ranks.
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) is a non-parametric method for comparing two independent samples on a single outcome variable.
Instead of comparing means like a t-test, it ranks every score across both groups together, then checks whether one group’s ranks cluster higher than the other’s.
It works with ordinal data (Likert-scale ratings, rankings) and with continuous data that is skewed, has outliers, or comes from a small sample.
Because it uses ranks rather than raw values, tied scores are handled by averaging the ranks they would otherwise occupy, which keeps the calculation fair.
Choose the Mann-Whitney U test when you have two independent groups, an ordinal or non-normal outcome, and a sample too small to trust the central limit theorem.
Typical dissertation examples include comparing satisfaction ratings between two clinics, exam scores between two teaching methods, or reaction times between two skewed experimental conditions.
For matched or repeated-measures data, use the Wilcoxon signed-rank test instead; for three or more independent groups, use the Kruskal-Wallis test.
Our guide to choosing the right statistical tests maps every option against your data type, design, and research question.
Both tests compare two independent groups, but they rest on different assumptions and can produce different conclusions from the same dataset.
| Feature | Mann-Whitney U Test | Independent T-Test |
|---|---|---|
| Data type | Ordinal, or continuous but non-normal | Continuous, normally distributed |
| What it compares | Rank distributions between groups | Group means |
| Key assumption | Independent observations; no normality needed | Normality and roughly equal variances |
| Sensitivity to outliers | Low — ranks limit their influence | High — raw means are pulled by outliers |
| Typical output | U statistic, z, p-value | t statistic, degrees of freedom, p-value |
If you are unsure whether your data meet t-test assumptions, our guide to understanding t-tests explains how to check normality and equal variances first.
The test follows a fixed sequence: rank all scores from both groups together, sum the ranks per group, then calculate U from those rank sums.
Software then compares the smaller U value against a critical value, or converts it to a z-score for larger samples, to produce a p-value.
Here is the ranking mechanic in practice, using ten hypothetical weekly revision-hour scores split evenly between two teaching groups.
Group A’s five values collect ranks 1, 3, 4, 6, and 9; Group B’s five values take the remaining ranks. Those rank sums feed straight into the U formula.
The test needs independent observations, meaning each participant appears in only one group and scores in one group cannot influence scores in the other.
Your outcome variable must be at least ordinal, so values can be meaningfully ranked from lowest to highest across both groups combined.
To compare medians directly, the two distributions should have a similar shape. If shapes differ sharply, the test still detects a difference, but the finding is about distributions generally, not medians specifically.
A p-value only tells you whether a difference is likely real; it says nothing about how large that difference is in practical terms.
The common effect size is r, calculated as the z-statistic divided by the square root of the total sample size (r = z / √N).
Conventional benchmarks treat r around 0.1 as a small effect, 0.3 as medium, and 0.5 or above as large, though discipline norms vary.
Because it does not assume normality, the Mann-Whitney U test can be used with fairly small samples, sometimes as few as five per group.
Very small samples do reduce statistical power, meaning a real difference between groups is more likely to go undetected than with a larger dataset.
Where possible, run an a priori power calculation before data collection so your dissertation methodology can justify the planned sample size.
In SPSS, go to Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples, then move your outcome variable into the Test Variable list.
Move your grouping variable into the Grouping Variable box, define the two group codes, tick Mann-Whitney U under Test Type, then click OK.
SPSS outputs a ranks table showing the mean rank per group, plus a test statistics table with the U value, z, and asymptotic significance.
Check the “Asymp. Sig. (2-tailed)” row in the test statistics table. A value below 0.05 usually indicates a statistically significant difference between groups.
A significant result means the two distributions differ, not necessarily their means. Report which group had the higher mean rank from the ranks table.
Always pair the p-value with an effect size, such as r calculated from the z-score, so readers can judge practical, not just statistical, significance.
For very small samples, SPSS can calculate an “Exact Sig.” value under Exact Tests rather than relying on the large-sample z-approximation, which is more accurate.
APA style reports the U statistic, both sample sizes, and the p-value, for example: U = 8, n1 = 5, n2 = 5, p > .05.
Report medians and interquartile ranges for each group rather than means, since the Mann-Whitney U test concerns rank distributions, not averages.
Do not report group means when using the Mann-Whitney U test; report medians instead, since the test does not assume symmetric distributions.
Do not equate a small p-value with a large effect; always check the effect size alongside statistical significance before drawing conclusions.
Do not apply this test to paired or repeated-measures data; that calls for the Wilcoxon signed-rank test instead, a related but distinct procedure.
Do not skip the assumption check; running Mann-Whitney on data that actually meet t-test assumptions can throw away statistical power you did not need to lose.
The Mann-Whitney U test is one option among several non-parametric procedures for comparing groups when parametric assumptions do not hold.
Getting test selection right early saves rework later, since switching tests after analysis can mean redoing your results and discussion sections from scratch.
Browse more walkthroughs like this one in our statistical analysis guide hub, covering everything from hypothesis testing to regression.
Selecting the right test, checking assumptions, and writing up results correctly takes real time when a dissertation deadline is close.
Our statistical analysis service covers test selection, SPSS output interpretation, and results write-ups for any UK academic level.
Our SPSS data analysis help is available for individual chapters or full projects, and our dissertation writing service can support the surrounding chapters.
It tests whether two independent groups differ on an ordinal or non-normally distributed outcome, by comparing the ranks of combined scores rather than raw means. It is the standard non-parametric alternative to the independent t-test, widely used in dissertations, surveys, and small-sample research designs across UK universities.
Use it when your outcome is ordinal, your continuous data are skewed or contain outliers, or your sample is too small to assume normality with confidence. If those assumptions hold instead, an independent t-test is usually more statistically powerful, so always check assumptions before deciding which test to run.
Go to Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples, add your outcome variable as the test variable and your grouping variable, define the group codes, tick Mann-Whitney U, then click OK. Read the p-value from the Asymp. Sig. (2-tailed) row in the output.
Mann-Whitney U compares two independent groups, such as separate cohorts or conditions. The Wilcoxon signed-rank test compares two related or paired measurements from the same participants, such as before-and-after scores. They are not interchangeable, so confirm your study design before choosing between them.
It means the ranked distributions of the two groups differ more than chance would predict, so one group tends to score higher than the other overall. It does not confirm the group means differ, and should always be reported alongside an effect size and the group medians.
Report the median and interquartile range for each group, not the mean. The test is based on ranks rather than raw averages, so medians better reflect what the analysis actually compared, and reporting means alongside a rank-based test can mislead readers about what was tested.
You May Also Like
All work is written by human writers. 100% AI free, guaranteed.
100% money back guarantee if you find plagiarism in our work.
COMPANY DETAILS
