The Wilcox Sign Test (or Wilcoxon signed rank test) requires two repeated measurements on a commensurate scale. That is that the values of both observations can be compared. If the variable is of metric (interval or ratio) scale the differences between both samples need to be ordered and ranked before conducting the Wilcox sign test.
The Wilcox Sign test makes four important assumptions
1. Dependent samples – the two samples need to be dependent observations of the cases. The Wilcox sign test tests for differences between a before and after measurement while accounting for individual differences in the baseline.
2. Independence – The Wilcox sign test makes the independence assumption, that the paired observations are randomly and independently drawn. That means that each pair of observations is independent from the other pairs of observations.
3. Continuous dependent variable – Although the Wilcoxon signed rank test ranks the differences according to their size and is therefore a non-parametric test, it assumes that the measurements are continuous in theoretical nature. To account for the fact that in most cases the dependent variable is binominal distributed a continuity correction is applied.
4. Ordinal level of measurement – The Wilcox sign test needs both dependent measurements to be at least of ordinal scale. This is necessary to ensure that the two values can be compared and for each pair it can be said if one value is greater, equal or less than the other.
Furthermore in order for the differences between measures to be rankable the observations must be comparable, that is for every difference of observations it must be clear which one is greater of if both observations are equal.
The test of significance of the Wilcox test further assumes that both samples have a continuous distribution function. This implies that tied ranks can not occur. However if tied ranks exist in the sample a continuity correction can be calculated. It is also possible to use an exact test that relies on permutation testing.
The big advantage of using a permutation tests to test of significance is that it does not assume a theoretical distribution for the test value, e.g. that z is normally distributed, and thus the test do not need to make any assumptions about the variables. This requires the sample size to be > 60. SPSS offers the option to use an exact test to calculate the test of significance of Wilcoxon’s W.
Since the Wilcoxon signed rank test does not require multivariate normality or homoscedasticity it is more robust than the dependent samples t-test. Apart from the cases where the two samples are not normally distributed it is better to use the Wilcox Sign Test when the sample includes outliers or heavy tails, two effects that highly influence the t-test.
