Hi,
In our study, we have assessed 116 participants. Basically we were measuring performance in a modified and non-modified version of a task, where higher amount of points indicated better performance. All the participants completed both versions, that is 52 of them completed the non-modified version first, whereas 64 completed the modified one first.
The same people were assessed 2-3 weeks after the first assessment with a version of a task they have not yet encountered.
Our aim is to check whether people differ in their scores, depending on the task version. Thus, we take a within-person approach. We would also like to control for the order somehow, and if that is even possible, for the practice effect, which presence was indicated by simple parametric tests (t test).
We were thinking about setting up a SEM model in MPlus, yet I wonder which modelling approach would be appropiate in those circumstances, as well as, if our sample size is not too small for SEM approaches. Other case being only 2 time points, as more measurements could broaden up the analytic possibilities. I would very much appreciate your insight and suggestions.
Thank you in advance!
Best
IMO, using SEM for a simple design like yours is a bit like using a sledge hammer to swat flies. Because you have complete data for all subjects, you could simply use a two-factor "mixed design" ANOVA model. The repeated measures factor is Task (non-modified vs modified); and the between-Ss factor is Order (1 = non-modified task first, 2 = modified task first). The ANOVA model will give you F-tests for the main effects of Task and Order, but also an F-test for the Task*Order interaction. The F-test for the interaction tests the null hypothesis that the effect of Task (i.e., the mean difference between non-modified and modified tasks) does not depend on the order in which the tasks are done. Putting that another way, H0 for the interaction says that the difference in differences = 0.
Note that you could also use a linear mixed model (LMM) to estimate the same model. If you use restricted maximum likelihood (REML) estimation, it duplicates the OLS model exactly when you have complete data. One advantage of using a LMM is that it uses all available data for each subject, whereas OLS models typically give you a complete case analysis.
Finally, if you say what software you use, someone might be able to direct you to relevant examples. HTH.
You could simply do a mixed between x within ANOVA with Order as a betwen independent variable and Task (modified vs. nonmodified) as a within variable. You could compute the respective within and between eta-squares for size of effect.
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