Whenever I have two samples (A and B), I've been doing conventional t-test to compare the significant difference in means if I find that these two sample come from normal population (using normality tests like JB). If they fail the normality test, I go with mann-whitney test.
I have a very basic doubt. If I have A and B, can I re-sample N times for both A and B with replacement, obtain their means and standard errors, and then test whether these two means (which are means of means obtained from re-sampling N times) are statistically different from each other using t-statistics. As if I am allowed to do so, essentially I am taking out the outliers from both A and B which should make my test more robust.
What can be the limitation of such approach. And if it can be applied, how the t-statistic can be modified? I've read about bootstrap hypothesis testing but due to some reason, I do not want to pool both A and B together. Rather I'd prefer the approach I mentioned above.
Please let me know your thoughts on the same. Thanks in advance.