Assumptions of the Wilcoxon Sign Test
The Wilcoxon Sign Test requires two repeated measurements on a commensurate scale, that is, that the values of both observations can be compared. If the variable is interval or ratio scale, the differences between both samples need to be ordered and ranked before conducting the Wilcoxon sign test.
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The Wilcoxon Sign test makes four important assumptions:
1. Dependent samples – the two samples need to be dependent observations of the cases. The Wilcoxon sign test assess for differences between a before and after measurement, while accounting for individual differences in the baseline.
2. Independence – The Wilcoxon sign test assumes independence, meaning that the paired observations are randomly and independently drawn.
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 Wilcoxon 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. 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 Wilcoxon test further assumes that both samples have a continuous distribution function. This implies that tied ranks cannot 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 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 Wilcoxon Sign Test when the sample includes outliers or heavy tails, two effects that highly influence the t test.
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