# ANOVA versus Wilcoxon

I need some help as a reviewer is giving me a hard time with the statistics...

I have 2 groups (A and B) where A has received a certain intraoperative treatment and B has not.

Now I measure pain postoperatively using numeric rating scales (from 1 to 10) at 5 different time points in the postoperative course.

I am actually interested in the comparison of the mean NRS scores between the two groups at each individual time point and I am not interested in comparing the values over time (e.g. timepoint 1 versus timepoint 5).
So I have used Wilcoxon signed rank test.

Now the reviewer states the following (I apologize for the capital letters but that is how I received the comment):

"THIS IS NOT THE CORRECT STATISTICAL ANALYSIS SINCE AN ANOVA FOR REPEATED MEASURES HAS TO BE CARRIED OUT, MAYBE CONSIDERING ALSO SOME TRANSFORMATION OF THE VARIABLES. THE CONSIDERED TEST COMPARED THE SAME GROUP AT TWO TIME POINTS (TWO REPEATED MEASURES) AND IN THIS CASE, WE HAVE TWO GROUPS OF RANDOMIZED PATIENTS AND FIVE TIME POINTS."

Is he wrong or do I not get it? Is it considered a repeated measure even if I am only interested in the pairwise comparison at each time-point and not in a comparison of different time points?

How should I respond?

Unless you've left some information out, it looks to me like you're both wrong.

I agree that if you're just comparing the two groups within a time point, this would not be repeated measures (though it's not clear to me that this comparison is necessarily valuable, I'll have to take your word for that).

If you're picking a time point and saying "how do A and B compare" then the values in A and in B would not seem to be paired. That would be independent samples, wouldn't it?

As such, I don't see how the signed rank test applies.

[However, if you're repeating the comparison at several time points, I don't know that separate models/tests is necessarily the ideal choice; that may depend in part on exactly what information you seek/what conclusions you're trying to draw]

It's of course difficult to know how to respond to a reviewer without understanding the full scope of the analysis and manuscript, but I have a couple of thoughts.

Since your dependent variable is measured on an ordinal scale of 1 to 10, the reviewer is probably off the mark suggesting you find a "transformation" presumably to change the variable to one that is approximately marginally normal.

Your instinct to use a nonparametric test was a good one. But the reviewer does have a point that it usually is desirable to put all the measurements together in one model.

There may be a nonparametric model to handle this design, but I'm not aware of one. Friedman or Quade won't work. There are some options discussed in Feys 2016, but I'm not really familiar with them.

My advice would be to use ordinal regression, which will allow for mixed effects to take into account the fact that there are multiple measurements on the same subject. The ease of conducting ordinal regression differs with different software packages. It's rather easy and flexible in R.