Using SAS 9.4.
16 animals were randomly assigned to two treatments (control and treatment). Each animal had its level on the dependent variable measured 24 times over the course of the day. For each animal, these numbers vary wildly, from 0 into the thousands, with no strong correlations.
Interest is in whether the two treatments are different.
I compared three models:
a) T-test on total activity level
proc ttest data = wide; class group; var total; run;
b) A multilevel model with unstructured covariances
title "MLM for day 1, unstructured covariance, only group entered"; proc mixed data = long; class group mouse_id; model act = group/solution; repeated/type = un subject = mouse_id; run;
c) A multilevel model with AR(1) covariances
title "MLM for day 1, AR1 covariance, only group entered"; proc mixed data = long; class group mouse_id; model act = group/solution; repeated/type = ar(1) subject = mouse_id; run;
c) Had slightly better AIC and BIC than b).
The effect size of group was roughly equal across all three models (after accounting for the fact that the t-test was on 24 values added up) but the standard errors for b) and c) were wildly different. b) Was significant, a) and c) were not.
In the past, I've not seen such huge changes in the standard errors.
Any thoughts on why this might occur and what to do?
NOTE: It's the same data, just one in long format and one in wide format.