[Joseph Coveney]

. . .my questions first. The results of the -testparm- do not convey the same information as those from the random effect model. The coefficients in the random effect indicate the average score changes from pre to po1/po2 under each condition (e.g. 1.condition#0.period, 1.condition#1.period). But the -testparm- outcomes compare the score changes between po1's change and po2's change under each condition, or the pre to po1/po2 score changes attributed to varied conditions. Did I interpret the outcomes correctly?

I can't quite follow you fully except to say that (1) the two testparm commands that I showed above in #12 address your two primary research questions and (2) the testparm command that you showed in #13 does not address either of your two primary research questions and its result is therefore irrelevant. What do the two examples of the testparm commands that I gave above in #12 show?

Furthermore, is the test comparable to what repeated anova does? . . I was asked why I didn't perform a repeated ANOVA first to examine whether the condition#period interaction term shows differences.

The answer to whoever asked you is (1) it isn't necessary or even desirable to fit a repeated-measures ANOVA either before or after fitting the random effects linear regression model. It doesn't add anything to the analysis and it doesn't help address your two primary research questions over and above the code that I gave above in #12. And (2) it isn't necessary or even desirable to first test whether the overall condition × period interaction term is "statistically significant" in order to assess your two primary research questions, which I assume were specified a priori.

To figure out the differences in using random effect and repeated anova, I ran following commands and got corresponding outcomes: . . . According to repeated anova, it shows there are no sig dif in srs scores between condition*period groups. However, this is not consistent with the random effect outcomes. How should I interpret their inconsistency? . . .Is it more comparable to what the random effect model did?

Neither of your syntax examples for repeated-measures ANOVA is correct. Regardless, repeated-measures ANOVA is not what you want in order to assess your two primary research questions. The code that I showed for xtreg (you can add the time-invariant covariates), followed by the two postestimation testparm examples, will get you most directly to the assessments that you seek.

The next step would be to forgo all of the distraction over repeated-measures ANOVA and plot the marginal effects using marginsplot which I believe will be invaluable to interpretation of the results of your study.