Questions the Wilcoxon Sign Test Answers

The Wilcoxon Sign Test is used to determine whether the mean ranks of two dependent, or matched, samples are different from each other.  This is the non-parametric alternative to the dependent sample t-test.  Technically, it tests if the average difference of a continuous variable that is measured twice is zero.

Management studies: Does introducing a brown bag lunch 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.

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 or if the sample size is small This happens especially if the subjects for the drug trial have not been chosen randomly.

Education: Does an 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 on the same population, and 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.