Question

Detail the steps in computing the Wilcoxon matched-pairs signed-rank test with a brief discussion specific to the important aspects of each step.

  

Answer 1

The Wilcoxon matched-pairs signed rank test computes the difference between each set of matched pairs, then follows the same procedure as the signed rank test to compare the sample against some median.

Assumptions:

1) Data are paired and come from the same population.

2) Each pair is chosen randomly and independently.

3) The data are measured on at least an interval scale when, as is usual, within-pair differences are calculated to perform the test.

Steps:

The first step of the Wilcoxon sign test is to calculate the differences of the repeated measurements and to calculate the absolute differences.

The next step of the Wilcoxon sign test is to sign each rank. If the original difference < 0 then the rank is multiplied by -1; if the difference is positive the rank stays positive.

The next step of the Wilcoxon sign test is to sign each rank. If the original difference < 0 then the rank is multiplied by -1; if the difference is positive the rank stays positive.

The next step is to calculate the W+ and W-.

W+ = Sum of positive ranks

W- = Sum of negative ranks

The shortcut to the hypothesis testing of the Wilcoxon signed rank-test is knowing the critical z-value for a 95% confidence interval (or a 5% level of significance) which is z = 1.96 for a two-tailed test and directionality. Whenever a test is based the normal distribution the sample z value needs to be 1.96 or higher to reject the null hypothesis.