How to Report a Mann-Whitney U Test (With Example)


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

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