Please help! T-test results & interpretation

Hi, please help me with this simple question that no one at my uni seems to be able to answer!

I have 3 groups (n=20) where I'm looking to establish differences pre & post treatment (2 intervention groups, 1 control). All are normally distributed.

I have done paired sample t-tests on all 3 groups which are all non-significant (p=0.05)

Am I right to assume that I can accept my nul hypothesis (Ho= No change) from the t-test results?

I am being told that I need to do an ANOVA analysis anyways - even if my t-tests are non- significant but I can't see the point. Is that the case?

Please help, I can't find any books to clarify the point and I'm really confused!



TS Contributor
Power in the repeated measures ANOVA (n=60?) is higher than in the three single
group tests (n=20 each). So with n=60 you might find a pre-post (main effect for "time") difference where your three single tests didn't.

And/or it might happen, for example, that the control group changes
negatively, but not enough to reach significance. And at the same time
experimental groups change positively, but not enough to reach significance. But
taken together, both changes might constitute a significant group*time effect in a
repeated measures (mixed) ANOVA.




No cake for spunky
If you do t-test multiple times with the same data sets your nominal alpha level will be incorrect. For example if you have an alpha level of .05 and you do two ttest you true alpha level wil be .025. So a p value of .03 will be below your nominal alpha level (the one you set initially) but above the true alpha level caused by doing two ttest with the same data. That is why the reccomendation was made (although if all were non-signficant it should not matter).