Mann-Whitney U and Wilcoxon

1. Aims and Learning Objectives

The aim of this workshop is to use SPSS to carry out both Mann-Whitney U and Wilcoxon statistical tests.

After this workshop you will be able to:

Use SPSS to carry out both Mann-Whitney U and Wilcoxon statistical tests.
Distinguish when a Mann-Whitney U should be used and when a Wilcoxon should be used.
Produce illustrative statistics for both tests.
Copy and paste the illustrative statistics into Microsoft Word.

2. The Mann-Whitney U and the Wilcoxon Statistical Tests

The Mann-Whitney U and the Wilcoxon statistical tests are non-parametric alternatives to the Related T-test and the Unrelated T-test. They both examine two sample data sets and enable us to decide whether they are statistically different from each other. The data must be at least Ordinal.

3. What is the Difference between the Mann-Whitney U and the Wilcoxon tests?

The difference between the Mann-Whitney U and the Wilcoxon tests relates to the design of the experiment. If your experiment has a repeated measures or matched participants design then the Wilcoxon test is used to analyse your data. If your experiment has an independent measures design then the Mann-Whitney U test is used to analyse your data.

4. Scenario 1: Drunk in Charge of a 747

20 pilots were placed in a flight simulator and required to land a 747 under very adverse weather conditions. One group of 10 had been given a pint of lager before they made their attempt at landing. The other 10 had been given a pint of non-alcoholic lager. A panel of judges made an estimate of their quality of landing (the higher the score the worse the attempted landing).

Task 1: Decide on your hypotheses (and whether they are one or two-tailed). What statistical test are you going to use for this experiment?

5. Mann-Whitney U

Check that Mann-Whitney U is already selected.
Click on OK.

The following tables should now appear in the Output window.

6. Illustrative Statistics

Bar charts are used to illustrate data when comparing the difference between two sample sets. Hence, bar charts are the most appropriate illustrative statistic when using the Mann-Whitney U or the Wilcoxon tests to analyse your data. When creating the illustrative statistics remember that the procedure is different when the design of your experiment is independent measures. Remember that when you are using repeated measures your bar chart data illustrates summaries of separate variables. When you are using independent measures your bar chart data illustrates summaries for groups of cases.

7. Scenario 2: Holidays

Ten people were asked to rate two top holiday destinations on how much they wanted to visit (1 being not at all, 5 being a must). A test was conducted to see whether the two destinations were favoured differently.

Task 3: Decide on your hypotheses (and whether they are one or two-tailed). What statistical test are you going to use for this experiment?

8. Wilcoxon

The following tables should appear in the Output window.

This table displays the mean ranks as well as the n value.

The Test Statistics table displays the test statistic Z.
As well as its significance value.
Task 4: From the values given, decide whether you are going to accept or reject the null hypothesis.
Task 5: Produce the illustrative statistics and import them into Microsoft Word.

Illustrative statistics are further required to augment the results and add understanding of the Wilcoxon results. Bar charts are used to illustrate data when comparing the difference between two sample sets. Hence, bar charts are the most appropriate illustrative statistic when using the Wilcoxon tests to analyse your data. Remember that when you are using repeated measures your bar chart data illustrates summaries of separate variables. When you are using independent measures your bar chart data illustrates summaries for groups of cases.

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Mann-Whitney U and Wilcoxon