# Applying a post hoc Wilcoxon signed rank test to a Friedman when there are different sample sizes

I conducted a Friedman test to related-sample group in three conditions (pre-treatment, post-treatment and 6-month post treatment). Out of 216 participants that completed the first two stages, 50 of these completed the 6-month post stage. Am I right in thinking that the Friedman test is doing the calculation on the 50 participants that completed all stages?

My problem is that I then want to conduct a Wilcoxon signed ranks post hoc test to examine where the differences are. N = 216 participants as opposed to the 50 used in the Friedman test.

Could anyone tell me if it is ok to use this result? Or do I have to separate the data further so the Wilcoxon test uses the 50 participants? Does this impact its validity?

Any help would be greatly appreciated,

Sam

• Friedman test is not the extension of Wilcoxon test on several related samples (it is closer to be the extension of sign test). So, it is very questionnable whether post-hoc pairwise comparisons corresponding to Friedman may be Wilcoxon tests. – ttnphns Dec 28 '13 at 15:41
• +1 @ttnphns. However in this particular setting with so many drop outs, the choice between post-hoc sign-tests or post-hoc Wilcoxon sign rank tests seems to be a minor problem. – Michael M Dec 29 '13 at 11:30

For post-hoc test you only should use those data that you previously used in Friedman, so all three pairwise compared groups should be of the sample size 50. The critical value of the test should also be adjusted by factor (m-1) where m is the number of groups. Holding the level of the type I error is at the expense of the power of the test.

• Why do you multiply the significance level by a factor of $(m-1) \cdot m$? – Michael M Dec 29 '13 at 15:11
• Thank you @Germaniawerks. I am unsure of the latter part of your response, m-1? – Samantha Goswell Dec 31 '13 at 14:02