RE: Permutation test with small number of possible permutations

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] Permutation test with small number of possible permutations Date: Sat, November 27, 2004 1:48 am Samer A A A A B B B B B B B B A A A A are equivalent, solutions will differ by the sign of the effect or, equivalently, by the class label only (for example, CL_A > CL_B versus CL_B > CL_A). A general formula for the number of permutations (for two classes A and B) is N! /( K!*(N-K)!), where N is the number of subjects, K is the number of elements in class A. But in this particular case, the number of elements in classes A and B are the same. This creates an additional symmetry. This symmetry can be used to reduce the number of permutations. You can use 70 permutations, if you like, but the result will be the same. If you like to use 70, just replace the first line of the script (i <- 1) by for(i in 1:5) A more general script (for more than two classes) is more difficult to write, I did it at some point in FORTRAN but I do not have it handy now. I am not sure that your interpretation of the variance is correct. These 35 (or 70) permutations are not random: they are carefully chosen to represent all possible permutations. Thus, they give you an exact distribution, equivalent to the infinite number of random permutations. You cannot use binomial sd(p) formula in this situation. Leonid