You cannot perform t-test, because it would treat the 3 measurements of the 25 subsjects as if there were 75 independent subjects. You could use repeated-measures analysis of variance, with 2 within-subject factors, "time point" (3 levels), and "time of measurement" (pre vs. post intervention).

Mind that a non-significant result for "time of measurement" would not proof that there is no change between pre and post. There may be an effect, but the test failed to detect it, for example due to too low statistical power (absence of evidence for an effect is not evidence of absence). "Proof" of absence would require an -> equivalence test approach, which is not easy to carry out and probably needs a much larger sample size

In the second case, a simple approach would be 2 separate repeated-measures ANOVAs, each with the repeated-measures factor "time point" (t0/t1 and t0/2, respectively), and in each analysis you add time between t0 and t1 (or t2, respectively) as a interval scaled predictor.

With kind regards

Karabiner

Karabiner, thank you for your reply.

Sorry about that I think I have to clarify my backgrond information first.

In fact my study is a multi-inventional study. I am going to see how the improvement is after i did the interventions to show these interventions have a positive outcome. Afterward, I have done a small optimization in the interventions and i would like to have sub group analysis between the pre-optimization and post optimization.

Therefore, I wound have 3 sets of data from t1, t2, t3 in which there are variations between t1-t2 and t2-t3 of different subjects. What I want to show is a general increment of the data.

AND also is there any improvement of efficancy after the optimization. So for the subgroup analyze, I would divide my data into 2 to see which one is superior to the other. This is what I most confusing with, as I would like to try to elimiate the factor of time, can I calulate the rate of change of T1-T2 and T2-T3,and also T1-T3 to show 1) there is a improvement of overall rate (T1-T3) AND 2) there is an improvement of rate at specific time (T1-T2 or T2-T3).

IF rate of change cannot be used, may be I just compare the % change ?

In addition, during the time of collection of data (t1,t2,t3), this is another pre/post test for a single intervention (what i mentioned before that I want to show there is no significant change among the pre/post test), as it is somehow not related to time, i just want to show the instant effect of that intervention, so probably I can just treat as 25* 3 tests which is independent of time?