# Can Ordinal data have a difference in mean if one is comparing the same group at different points in time?

I'm currently looking at a study where Ordinal scales are used to compare the effects of drugs on Alzheimer at different time points throughout treatment https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5974972/pdf/main.pdf

I've always understood that one can't meaningfully calculate a Mean for Ordinal data since the difference between the levels of the scale aren't equal. Yet here they seem to be using a Mean to explain the difference at different time points in the same group.

For example on Page 7: For the Placebo group in Study 1, they take the ADAS-Cog scale Mean of Week 12 of 124 patients and minus it from the ADAS-Cog Mean of Week 0 of those same patients and get -0.1 (All of it Adjusted) or -0.3 if we compare Week 24 and 0. At least I assume it's subtracted since the ADAS-Cog scale itself at the lowest can ever go to 0 not negative numbers (please correct me if I'm wrong)

I'm trying to understand what this Adjusted Mean actually means and how it's calculated if Ordinal data can't have a Mean. Are they just throwing common sense out of the window and deciding to treat the ordinal scale numbers like normal interval numbers?

It says "Primary inference was conducted using a mixed model for repeated measures analysis using restricted maximum likelihood estimation". Does this allow to use means for ordinal scales when comparing the same group at different points in time? Thank you

P.S: I am not a statistician or anything but I do have a basic grasp on biostatistics.

• I think this question stats.stackexchange.com/questions/93680/… may answer your question as well. If not, please let us know what else you need. Jul 26 at 17:57
• Thank you for the taking the time to answer Peter. I gave your link a glance. It's a fair bit beyond my knowledge of statistics. Plus on top of that I'm trying to apply the information to my specific clinical study case in order to make sense of how the researchers of the clinical trial did it. I'll try to dig deeper and see if I can figure it out. There's a lot of new concepts to be learned from that thread. Thanks again. Jul 26 at 22:33