# Do I need to use weighted means with the Wilcoxon signed rank test?

I have 22 patients. They have been measured pre and post treatment. There are 3 measurements per patient before treatment (pre baseline), and four measurements after treatment (post baseline). There are also missing values.

Patient  pre1  pre2  pre3  post1 post2 post3 post4
1        3.2   2.7   3.3   5.9   NA    5.4   5.2
2        2.1   NA    3.4   6.6   5.3   6.8   5.7
...
22       3.5   NA    NA    NA    NA    2.3   5.3

I need to perform a Wilcoxon signed rank test to compare pre and post baselines. Since the number of pre and post data differ, I first calculate means of the pre and post values for each patient and then perform the Wilcoxon test on the two resulting vectors of means of equal length.

Pseudocode:

pre  <- c(mean(pre1.patient1, pre2.patient1, pre3.patient1), mean(c(pre1.patient2, ...
post <- c(mean(post1.patient1, ...

But due to the missing values, the number of values differ for each patient.

Do I need to use weighted means for the Wilcoxon signed rank test?

It would be great if you could provide a source for your answer, but not necessary.

• Do you mean to say that the 3 pre are comparable, i.e. they are 3 attempts to measure the same thing, and the 4 post are likewise comparable? – ttnphns Jan 10 '15 at 12:40
• Each measurement is a measure of symptom strength (e.g. subjective pain). The patients have to fill in a questionnaire on three consecutive days before, and on four consecutive days after treatment (e.g. "How strong was your pain today?"). On some days some patients do not fill in the questionnaire, resulting in missing data. Note: Sample data in question is fictional. – user14650 Jan 10 '15 at 12:43