I am comparing two sets of samples that are of different sizes (n) and are from two different populations. Both sets have undergone a similar intervention at different time periods (one from August to December and the other from January to April). Although both sets have treatment groups, this is not the typical one control and one experiment scenario. My objective is to study the mean of both samples.
To achieve this, I am using a two-sample t-test assuming unequal variances to deduce the p-value. If the p-value is less than 0.05, I will conclude that the difference is significant. Is this the right approach? Should I be using a t-test, and if so, which one? Additionally, would calculating Cohen's D be valuable in this case?
Please let me know if my approach is correct or if there are any other suggestions you would recommend.