Wilcoxon SignedRanks Test for Freshman 15 The following table lists some of the weights from Data Set 4 in Appendix B. Those weights were measured from college students in September and later in April of their freshman year. Assume that we plan to use the Wilcoxon signed-ranks test to test the claim of no difference between September weights and April weights. What requirements must be satisfied for this test? Is there any requirement that the populations must have a normal distribution or any other specific distribution? In what sense is this Wilcoxon signed-ranks test a “distribution-free test”?
In order to use the Wilcoxon sign-ranks test the following requirements must be satisfied:
(i) The data are a simple random sample.
(ii) The population of differences has a distribution that is approximately symmetric.
While using the Wilcoxon sign-ranks test, the sign of the differences and the magnitude of the difference is taken in to the account. So there is no requirement that the sample data came from a population with any particular distribution, such as normal distribution.
Wilcoxon sign-ranks test is a distribution free test; it’s used for the data which does not follow the normal distribution. Here only the sign of the difference and the magnitude of the signs is checked.