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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. enter image description here

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  • $\begingroup$ 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). $\endgroup$ – user2974951 Dec 21 '18 at 8:55
  • $\begingroup$ 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? $\endgroup$ – Candice Dec 21 '18 at 11:56
  • $\begingroup$ 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. $\endgroup$ – user2974951 Dec 21 '18 at 12:16
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This can be done using a linear model. Depending on the software you are using, you can either code the periods as a categorical variable which would result in an intercept and slope term for each and every period, which you can then compare between them using t-tests to get p-values for significance.

Alternatively, you could use the periods as an ordinal variable, if the software allows it. After that you would test whether there is a linear, quadratic or higher degree trend in your data using ordinal contrasts, and also get p-values.

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