- the scale of measurement has the properties of an equal-interval scale
- differences between paired values are randomly selected from the source population
- the source population has a normal distribution.
- The distribution of difference scores is symmetric (implies equal interval scale)
- difference scores are mutually independent
- difference scores have the same mean
The original measures are replaced with ranks resulting in analysis only of the ordinal relationships. The signed ranks are organized and summed, giving a number, W. When the numbers of positive and negative signs are about equal (i.e., there is no tendency in either direction), the value of W will be near zero, and the null hypothesis will be supported. Positive or negative sums indicate there is a tendency for the ranks to have significance so there is a difference in the cases in the specified direction.
Given a table name and names of paired numeric columns, a Wilcoxon test is produced. The Wilcoxon tests whether a sample comes from a population with a specific mean or median. The null hypothesis is that the samples come from populations with the same mean or median. The alternative hypothesis is that the samples come from populations with different means or medians (two-tailed test), or that in addition the difference is in a specific direction (upper-tailed or lower-tailed tests). Output is a p-value, which when compared to the user’s threshold, determines whether the null hypothesis should be rejected.