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Mann-Whitney test

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QXL Stat Tools Tab > Hypothesis Tests > Tests for Median > Mann-Whitney test

Test type: Median
Data: Quantitative
Number of Variables: 1
Number of Groups: 2
Assumptions: Two independent samples

The Mann-Whitney test is a hypothesis test for the significance of the difference between the two populations' medians. It assumes that two samples come from independent populations and that they have the same shape and equal variance. If the samples do not have equal variance, consider two sample t test with unequal variances.

Hypothesis tested:

H0 : Median1 = Median2
H1 : Median1 ≠ Median2

where Median1 and Median2 are the populations' medians.

Step #1: Select data source for Mann-Whitney test.

Data for the Mann-Whitney test can come from an Excel spreadsheet or SQL data source.

See source data formats and example data for the Mann-Whitney test.

Step #2: Options.

  • Standard options

    • 'Not equal to' option. Select this option to run a two tailed test. The null hypothesis is that the medians are equal.
    • 'Less Than' option. Select this option to run a lower tailed test. The alternative hypothesis is that the median of the first dataset is smaller than the median of the second dataset.
    • 'Greater Than' option. Select this option to run an upper tailed test. The alternative hypothesis is that the median of the first dataset is greater than the median of the second dataset.

  • Advanced options

    • 'Decision Criteria' option (default = 0.05). The value of the decision criteria (significance or α level).
    • 'Display mode' option. When the 'Verbose (long)' option is on, Quantum XL will display additional text that explains the hypothesis test results.

Example

  • Open Mann-Whitney worksheet.

  • Run Quantum XL > Hypothesis Tests > Tests for Median > Mann-Whitney.

  • In the Standard Options dialog, select 'Not equal to' test.

Mann-Whitney results

Quantum XL will display test statistic (W), p Value, p-Value when adjusted for ties, and dataset statistics.

In this example, p-Value of 0.00002 is less than the decision criteria (0.05), so the null hypothesis can be rejected. We can draw the conclusion that the medians are different.

Update

The Mann-Whitney test is updatable. After you create the analysis, you can change its data source or add new data to the data source and simply update the analysis.

  • Update: Quantum XL > Statistical Tools > Update Sheet

  • Change settings: Quantum XL > Statistical Tools > Modify Chart/Analysis