A Mann-Whitney U test is used to compare the differences between two independent samples when the sample distributions are not normally distributed and the sample sizes are small (n <30).
When reporting the results of a Mann-Whitney U test, we always use the following general structure:
- A brief description of the independent and dependent variable.
- The overall z-value of the test and the corresponding p-value.
Here is the exact wording we can use:
A Mann-Whitney U test was performed to compare [response variable of interest] in [group 1] and [group 2].
There [was or was not] a significant difference in [response variable of interest] between [group1] and [group2]; z = [z-value], p = [p-value].
The following example shows how to report the results of a Mann-Whitney U test in practice.
Example: How to Report Results of Mann-Whitney U Test
Suppose researchers want to know if a new fuel leads to a change in the average mpg of a car.
To test this, they conduct an experiment in which they measure the mpg of 12 cars with the new fuel and 12 cars with normal fuel.
To determine if there is a significant difference between the two groups, they perform a Mann-Whitney U test in SPSS and receive the following results:
The most important numbers in the output are the Z test statistic and the Asymptotic 2-tailed p-value:
- Z test statistic: -1.279
- p-value: .201
Since the p-value is not less than 0.05, we fail to reject the null hypothesis. We do not have sufficient evidence to say that the true mean mpg is different between the two groups.
Here is how we would report the results of this Mann-Whitney U test:
A Mann-Whitney U test was performed to compare average miles per gallon between cars that received a new fuel and cars that received regular fuel.
There was not a significant difference in average miles per gallon between between cars that received a new fuel and cars that received regular fuel; z = -1.279, p = .201.
Note: As a rule of thumb, we round p-values in the report to three decimal places. However, depending on your industry it may be standard practice to round to a different number of decimal places.
Additional Resources
The following tutorials provide additional information about the Mann-Whitney U test:
An Introduction to the Mann-Whitney U Test
How to Perform a Mann-Whitney U Test in Excel
How to Perform a Mann-Whitney U Test in SPSS
How to Perform a Mann-Whitney U Test in R
Hello,
I have a sample size of about n =18. I am so confused, do I use the U statistic table or the p value from the z table to make a decision on significance in a MWU test?
Great question — this confusion is very common, especially when dealing with smaller sample sizes in the **Mann-Whitney U Test (MWU)**.
### ✅ Here’s the simple answer:
**Use the U table for small sample sizes (usually when both groups have n ≤ 20).**
**Use the p-value from the normal (z) approximation when at least one group has n > 20.**
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### 🧪 Since your total sample size is n = 18 (likely something like n₁ = 9 and n₂ = 9):
You **should use the Mann-Whitney U critical values table** (i.e., the exact test, not the z-approximation) because:
* Your sample size is small.
* The normal approximation may not be accurate for small samples.
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### 🔍 What to do:
1. **Calculate the U statistic** from your data.
2. **Look up the critical U value** from a Mann-Whitney U critical values table for your n₁ and n₂ at your chosen significance level (e.g., α = 0.05).
3. **Compare your U statistic to the critical value**:
* If your **U ≤ critical value**, then the result is **significant** (reject the null hypothesis).
* If your **U > critical value**, then the result is **not significant**.
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### 📝 If you’re using software (like R, SPSS, Python):
* Many programs automatically report the **p-value using the normal approximation** with a **continuity correction**.
* In such cases, you can **report the exact p-value** *only if the software gives it*, or you may still **prefer the U table approach** for formal reporting in small samples.
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### ⚠️ Summary:
| Situation | Which to use |
| ————————————- | ————————————— |
| **n₁ and n₂ ≤ 20** | **Use U critical value table** |
| **At least one of n₁ or n₂ > 20** | Use **z approximation** and **p-value** |
| **Using software with exact p-value** | Use the **exact p-value** if available |
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