Wilcoxon rank sum test

Dear all,

I am facing another statistical issue and I hope someone out there can help me :-)

My data: 2 samples of companies, which were targets of a specific intervention at some point in time. I look at the development of a certain financial ratio in the years subsequent to the event. One sample contains targets of SUCCESSFUL interventions, the other entails targets of UNSUCCESSFUL events.

My task: I want to test for difference in both MEANS and MEDIANS between the ratios for the two samples in the various years subsequent to the event.

My approach: I am using the paired-sample t-test (ttest) for testing the means and the two-sided Wilcoxon rank sum test (ranksum) for testing the medians (as I am of the opinion that I am dealing with two independent samples).

My problem: The t-statistic (testing the difference in means) is very insignificant for all five years ex-post the event, which I was expecting. The z-statistic (ranksum), however, is highly significant for all years in question, even though for two of the five years the medians of the successful and the unsuccessful sample are almost identical.

My questions: Am I using the right tests? If so, can my results (especially for the test of differences in median) be correct and why? Are my samples (companies who have undergone successful interventions vs. unsuccessful interventions) independent? Or should I rather use the Wilcoxon SIGNED rank test?

Any help is much appreciated.

My best, Christian

Answer 1

[Star Strider]

The t-test assumes your data are normally distributed. The Wilcoxon rank sum test is nonparametric (although the statistic derived from it is normally-distributed, creating the z-score).

I would use histfit to begin with to see how your data are distributed, then choose the appropriate test.

[Christian]

Thanks for your quick reply, Star Strider.

I think, I didn't ask good questions. Put in a different way: - Are my samples (successful vs. unsuccessful) independent? They come from the same population (companies which have undergone interventions), however, one subsample has undergone successful interventions, the other unsuccessful interventions. - Would it make more sense to use the Wilcoxon Signed Rank Test in this particular setting?

[Star Strider]

The Wilcoxon rank sum would be my preference, since it does not depend on the samples being paired, whereas (according to my re-reading of Hollander, et al., Nonparametric Statistical Methods ISBN: 978-0-470-38737-5) the signed-rank test does.

I used the rank-sum test comparing simultaneous placebo-controlled medication effects from a population of randomly-chosen, similar individuals from a large group. It seems that your study might be similar enough to mine that the rank sum test would be appropriate.

I doubt that I have the necessary background to understand the details of your study design and data, so you have to fill in the necessary missing information to decide which is best. If you chose two groups of companies (ideally randomly) and did interventions on one group and not the other, then the rank sum is appropriate. If you compared the same companies pre- and post-intervention, then the signed rank is appropriate.

[Christian]

Hey Star, I made a mistake. Now my z-statistics make sense. I included ~isnan on both x and y in my ranksum formula. Really stupid :-(

Sorry for bothering you, and thanks again for your help Star! Much appreciated!

[Star Strider]

My pleasure!

You didn’t bother me at all! You did send me back to the books (always good, in my opinion) to review the two Wilcoxon tests and research their applicability to your data.