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I am trying to find what permutation size $B$ I should be using for conducting a permutation test. Currently I have two samples which are normal, same mean but different variance. The sample sizes are the same at $N_1 = 30$ and $N_2 = 30$. Obviously it is not feasible to find and evaluate each permutation as $60 \choose 30$ = 1.182646e+17. Hence, I am trying to find the upper bound on what I should make $B$. I noticed that there was already some literature and people have asked questions:

Required number of permutations for a permutation-based p-value

However, it seems that the upper bound doesn't depend on my sample size but rather the precision. Does anyone know why and how I may be able to obtain a reasonable bound for my sample size of 60? Thanks!

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    $\begingroup$ You're trying to calculate a proportion via what is effectively simulation (random sampling). Why would the sample sizes matter with respect to what that proportion is? $\endgroup$
    – Glen_b
    Commented Sep 24, 2015 at 2:58

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The intuition is for example, I have a sample size=10, if I permute it 500 times, it should generate a distribution more approximate the true distribution. Accordingly, the estimated p value is nearer the true p value. On the contrary, if the sample size is 100, 500 times permutation may cause a larger variance of the distribution of p value. I think this is the underlying logic of the question. But I have no answer rn.

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