[Jae Li]

@Joseph Coveney Hi Joseph, thank you a million for all the suggestions! Apart from cfi indicator, I have other indicator variables so when I applied the two permutation methods to those (the rest of codes remains unchanged), the mean difference T was different from true mean difference from two beta coefficients. Also, I found that the p-values changes every time when you have different

-reps()-

, so does it mean having the higher number of Monte Carlo permutations, we can obtain the more accurate approximation of mean differences and the lower approximation of p-values?

Many thanks to you!

[Joseph Coveney]

. . . when I applied the two permutation methods to those (the rest of codes remains unchanged), the mean difference T was different from true mean difference from two beta coefficients.

I'm not quite certain of what you're referring to as the "true mean difference", but if it is intended to mean that T differs from what you'd get by manually subtracting the coefficients, then you have made a programming error. I suggest that you and a colleague undertake a code review of your program.

. . . having the higher number of Monte Carlo permutations, we can obtain the more accurate approximation of mean differences and the lower approximation of p-values?

To quote the help file for permute, "permute reports the Monte Carlo error, which you can use to evaluate whether the specified number of permutations provides sufficient precision for the reported p-value estimates."