Comparing Z-Scores from Different Wilcoxon Signed Rank Tests I have paired dependent data that represent pre-intervention/post-intervention ordinal values for the participants of a study. As part of the study, I have three separate groupings of participants: A, B, and C. They all had different backgrounds and will be independent variables to the overall study, but experienced the same intervention. With this, I would like to compare the impact that the intervention had on the participants.
I ran 3 sets of Wilcoxon Signed-Rank Tests for three different variable pairs (var 1, var 2, and var 3) and received the following Z scores calculated with SPSS:





var 0
var 1
var 2




GroupA Z
-2.79
-2.1
-2.45


GroupB Z
-2.12
-2.04
-1.04


GroupC Z
-2.14
-2.66
-2.42




All of these values have a p-value of <0.05 except for GroupB/Var2.
Is there any way to compare these Z scores and make observations about the impact of the intervention across the groups to say that it's more effective for one group over another? If so, does it matter that one of the Z scores is not statistically significant?
 A: In your experiment you have three groups and three outcomes; each outcome variable is measured before and after an intervention. You performed 9 Wilcoxon signed rank tests to compare (paired) pre- and post-intervention values, one test for each combination of group and outcome.
The fact that one p-value doesn't reach significance is a bit of a red herring. If all 9 p-values were < 0.05, it wouldn't be any clearer how to compare meaningfully the intervention effectiveness across groups based on the 9 independent hypothesis tests. You haven't yet a made comparative analysis of the groups; from the provided summary we can only conclude that the intervention reduces the responses in all groups, possibly by similar amount (except for group B on response var 2).
Here is an alternative approach: For each variable, use regression to model the post-intervention measurement as a function of the group and the pre-intervention measurement. Since the variables are ordinal, use proportional odds regression which is a generalization of the Wilcoxon rank sum test. (Note: This is an analysis of post-intervention scores instead of analysis of differences between pre- and post-intervention scores.) The result will be a highly interpretable model that can make comparisons (aka estimate contrasts) between categories.
I acknowledge that this analysis looks at each outcome variable in turn rather than model the three outcomes simultaneously. Still, three regressions are more informative than nine hypothesis tests.
