Hi,

For your research question comparing EV concentrations in blood samples pre- and post-procedure, the Wilcoxon matched-pairs signed-rank test is apt as it's tailored for paired data. This test stands in contrast to the Wilcoxon signed-rank test, which compares medians against a hypothetical median. The variance between SPSS and GraphPad Prism outputs might stem from their employment of these distinct tests. Given your paired data, it's advisable to utilise the Wilcoxon matched-pairs signed-rank test for your analysis.

Hope this helps. 

I don't understand how you could apply the (one-sample) signed rank test with data from two samples, as this expected only a single sample. The matched-pairs signed-rank test is actually a (one-sample) signed rank test on the paired differences.

Hsin-Yuan Chen , "which compares medians against a hypothetical median" -- that's wrong. Wilcoxon tests are generally not about medians. These tests are about the stochastic equivalence. Only in very special cases this hypothesis is equivalent to defined hypothesis about the median(s), and in these cases they apply to means and modes as well. These special cases include symmetry and/or variance homogeneity of the distributions, what is very typically not the case when people are of the opinion that they ought to use these tests.

Michał Łomiak , as I wrote above, it's hard to use these tests to support directional claims - in your case claims like that the (expected) concentration in one group is higher (or lower) than in the other group. But this is typically what you want to conclude. If you want to make such claims from your data you should better use a t-test, possibly with the log concentrations, or a bootstrap-version of the t-test.

Jochen Wilhelm

Hi,

You're spot on, and I'm grateful for the insight. The Wilcoxon tests focus more on stochastic dominance than on medians. I erred in simplifying it as a median-based comparison. You're right about the specifics of symmetry and variance homogeneity. Thanks for the correction.

You are welcome. My intention is not to correct you but to avoid that readers take home wrong ideas. It is written and taught too often that the Wilcoxon tests are "alternatives" to the t-tests and that they are about testing medians - but this is wrong, at least in all cases where t-tests could also be applied.

Hello Jochen Wilhelm. I do not have my copy of Conover's book with me right now, so cannot check this, but the Wikipedia page on the Wilcoxon signed ranks test says this:

The one-sample Wilcoxon signed-rank test can be used to test whether data comes from a symmetric population with a specified median.[12] If the population median is known, then it can be used to test whether data is symmetric about its center.[13]

And reference 12 is:

Conover, W. J. (1999). Practical nonparametric statistics (3rd ed.). John Wiley & Sons, Inc. ISBN 0-471-16068-7. (See pp. 352–357)

AFAIK, Conover is a very trust-worthy source on "nonparametric" tests.

Furthermore, the Stat 500 notes from PennState (which I also find quite reliable) describe the one-sample Wilcoxon signed ranks test similarly, and show that Minitab has an option to carry it out:

• https://online.stat.psu.edu/stat500/lesson/11/11.1/11.1.2

That prompted me to check if SPSS has an option to compute this test, and it does (see attached image).

In conclusion, I agree with you about the two-sample test, which I believe is the much better known test (by far). But the one-sample test apparently does test a null hypothesis about a median.

PS- As the original question was about comparing (paired) pre-intervention and post-intervention scores, the paired test would be the one to use. But I agree with you that a paired t-test would likely be better. ;-)

To help show students that this is not about medians, I give this handout, where the KW shows no differences (the medians are all the same), but the pairwise MWs each show a significant difference. And I spent a while getting the colors to vary like that.

Bruce Weaver , that's correct -- for symmetric distributions, as you cited. This is exactly the case where mean, median and mode are all the same and a test of medians is also a test of means and also a test of modes. This is a case where the t-test seems preferrable (even in strange cases as for U-shaped distributions). However, the Wilcoxon test is typically proposed as an alternative hen the distributions are *not* symmetric...