I think this is a "meta-analysis" situation.
I've got 3 samples (from 3 studies); I've assumed that two are from population A (treatment A) and one is from population B (treatment B). I have the sample means, standard errors & sample sizes for each sample (and that's all). I want to test if the pop A mean equals the pop B mean.
I did t-tests for samples A1 vs B1 and A2 vs B1 and got p-values of like 0.6 and 0.3 respectively. What can I say about A vs B overall? How do I get an overall p-value for the null hypothesis $\mu_A = \mu_B$?
I can compute the sample mean of A1 union A2, by taking the weighted average of the two means. It would be nice if I just had the sample variance of A1 union A2, but I don't (I'd guess it's about equal to the sum of the A1 variance and A2 variance..).
[sorry I'm sure there's a bunch of answers to this on here and elsewhere, but I'm unable to identify/understand them]