The Wilcoxon Sign Test is used to determine whether the mean ranks of two dependent samples are different from each other. Technically it tests if the average difference of a continuous variable that is measured twice is zero.
There is generally two ways of pairing the observations (1) Before-After measurements, (2) pairing similar candidates.
The first group of pairings typically answers questions like:
- Medicine: Does the drug improve the health accounting for individual differences in health at the start of the trail? The Wilcoxon Sign Test is the ideal test when the participants have differences in their measurement baselines that might affect the outcome of the experiment. However, the pairing of the two samples needs to be designed into the experiment and needs some consideration before conducting it if the Wilcoxon Sign Test is going to be used. This test should be used when multivariate normality is not present in the data. This happens especially if the subjects for the drug trial have not been chosen randomly.
- Education: Does a innovative form of teaching help children to learn? The Wilcoxon Sign Test compares the results of the first test (with grades A-F) with the results of the second test, thus it accounts for different abilities that exist within the test takers. However this design needs to be controlled, because just retaking the exact same test might improve the scores. A Wilcoxon Sign Test on the performance of a control group can identify this effect and establish its significance. Here the test should be used because grading is an ordinal level of measurement.
- Management studies: Does introducing a brown bag lunch and learn improve employee satisfaction? The Wilcoxon Sign Test should be used when the improvement in satisfaction by introducing an activity like this would be overshadowed by individual differences in their initial satisfaction. However, this survey also needs to control for other factors that might have changed the employee satisfaction.
The second group answers questions like:
- Medicine: Does the drug improve the health accounting for individual differences in health at the start of the trail? This test can also be used if the pairing has not been explicitly defined, e.g., the measurement has been taken twice for one participant in a clinical study (before-after design). Another approach is to group the observations from a control and treatment group by similar characteristics that influence the outcome of the trial. For example if blood pressure, age, and cholesterol level are known to predict heart disease the Wilcoxon Sign Test can be used by pairing similar participants from the control with participants from the treatment group. Thus ensuring that individual differences do not overshadow the differences the treatment caused, and because the participants of the trial have not been chosen randomly (e.g., they presented with the illness) the independence and most likely the multivariate normality assumption of the dependent variable t-test are not met.
- Management studies: Does the introduction of flexible working hours help first time mother to better manage their work-life-balance? An approach to this question could be simply to ask them if you had flex time, or if flex time would be abolished, do you think you… However such a design never reveals the true impact. The most realistic answer can be found if two groups of first time mothers are compared, the ones with flex time at their work and the ones without. Using the Wilcoxon Sign Test instead of the Mann-Whitney U Test allows to group the participants of the research study into pairs with similar baseline, e.g., the researcher would pair two single mothers, two mothers with househusbands, two mothers with au-pairs etc. Thus accounting for individual yet typical differences in the baseline.
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Related Pages:
Conduct and Interpret a Wilcoxon Sign Test
What is the Wilcoxon Sign Test?
