12.4 Details & Notes

12.4.1 The Wilcoxon signed-rank test is considered a non-parametric test because it makes no assumptions regarding the distribution of the population from which the data are collected. This appears to be a tremendous advantage over the t-test, so why not use the signed-rank test in all situations?

First, the t-test has been shown to be a more powerful test in detecting true differences when the data are normally distributed. Because the normal distribution occurs quite often in nature, the t-test is the method of choice for a wide range of applications. Secondly, analysts often feel more comfortable reporting a t-test whenever it is appropriate, especially to a non-statistician, because many clinical research professionals have become familiar with the terminology. One reason the t-test has enjoyed popular usage is its robustness under deviations to the underlying assumptions. Finally, the Wilcoxon signed-rank test does require the assumption of a symmetrical underlying distribution. When the data are highly skewed or otherwise non-symmetrical, an alternative to the signed-rank test, such as the sign test (discussed in Chapter 15), can be used.