# Test to compare on an ordinal scale, two groups of data that have covariates

I have two (Test and Control) groups of data. Data in each group is divided into 10 (ordinal) period. In each of these periods, number of observation ranges anywhere from 22-53. The assumption is that values (coefficient of slope, intercept, mean) will decrease when going from Period 1 to Period 10. What is the best test for this?

1. Within each group, fit a linear model and extract coefficients for each period. Regress the coefficients against period 1-10. Run ANCOVA.
2. Same as above, but Run Wilcoxon test instead.
3. Within each period, compute the difference between test group and control group, then fit a linear model against period (1-10).
4. Any other better ways?

I have illustrated the data in the attached picture for clarity.

• Why not just estimate all the coefficient for each period in one single linear model? Then you can compare them against each other with the desired contrasts). Dec 21, 2018 at 8:55
• Do you mean first, estimate the coefficients for each period. And then in each group, regress the coefficients against period. The run a test to compare the difference between regression lines of the two groups? Dec 21, 2018 at 11:56
• You use one model, where you regress all the periods. The result is one model which returns one mean and one slope for each and every period. Afterwards you can perform post-hoc tests to check arbitrary hypotheses. Dec 21, 2018 at 12:16