Instead of sampling B times from each sample, we sample \sqrt from each of them and then take all pairs. Each bootstrap sample is independent of each other, hence there is no violation of the theory.
A vector with the test statistic and the bootstrap p-value.
Michail Tsagris and Christina Chatzipantsiou
R implementation and documentation: Michail Tsagris and Christina Chatzipantsiou .
B.L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.
Efron Bradley and Robert J. Tibshirani (1993). An introduction to the bootstrap. New York: Chapman & Hall/CRC.
Chatzipantsiou C., Dimitriadis M., Papadakis M. and Tsagris M. (2019). Extremely efficient permutation and bootstrap hypothesis tests using R. To appear in the Journal of Modern Applied Statistical Methods.
ttest2, exact.ttest2, ftest