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In his book "Resampling: the New Statistics" (available for free online), Julian Simon presents several examples where he Bootstraps the differences in group means, assuming that the observations of the two original groups came from the same population, with the purpose of null hypothesis testing.

Specifically, after observing group 1 with mean of x1, and group 2 with mean of x2, he combines the groups, and then resamples with replacement two new groups of the original sizes: sim_x1 and sim_x2, from the combined distribution. He then compares the bootstrapped/simulated differences in means with the empirical difference.

This is very similar to randomization tests, with the exception that the simulated groups can have repeated values.

However, I have not found anyone else suggesting this application of the Bootstrap. People seem to suggest either the use of Randomization tests, or Bootstrapping separately within groups after equalizing their means (x1 - x1.mean + pooled_mean; x2 - x2.mean + pooled_mean).

Is Simon's method flawed?

Edit: This method is presented -- but ignored in the discussion -- in this thread (the author calls it Bootstrap 1)

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