I'm using the bootstrap method to test my experiment results for significance. I have two sets (say A & B) of 50 grades, for which I want to test whether their means are significantly different. The method I often found while searching for similar problems, is defining a statistic, e.g., mean(A)-mean(B) and checking whether the bootstrapped sampling distribution overlaps zero.
However, I read about another method as well. Here, bootstrapping is applied to the combined grade sets A & B, thus a bootstrap sample is randomly picked from all grades combined. After bootstrapping, checking whether the means of A and B are within the tails of the combined bootstrap distribution would determine whether sets A and B are significantly different. The argument was that, if A and B would not be significantly different, the bootstrap method would show that they both belong to the same distribution.
The second method sounds correct to me, can someone confirm or refute this method?