Greg and Marc,
Not that it's needed here but, of course, perm.test() in pkg:exactRankTests or oneway_test() in pkg:coin can be used. Using Marc's / Greg's computations, the (two-sided) p-value is sum(abs(perms) >= abs(orig)) / length(perms) [1] 0.01937395 perm.test() and oneway_test give a p-value of 0.003249691, using the "exact" option. Question: Why the difference? Answer: perm.test() uses the *mean* difference instead of the median difference. (Easy to check: just replace 'median' with 'mean' in Marc's computation of perms.) As Greg correctly points out, different test statistics can sensibly be used. But which statistic, mean difference or median difference, is more appropriate for the given data? Assumptions: 1. the null hypothesis is that the two sets of observations represent random samples from the same distribution; 2. the range of the distribution consists of a small set of integers. Fire away! Peter Ehlers Greg Snow wrote:
Thanks Marc, The sampling is so easy that I often forget that we can do the exact permutation test for smaller samples (and I can never remember when small is small enough for this). With the exact permutations we really don't need to do the prop.test or binom.test, I usually do that to get the confidence interval on the p-value due to sampling from the permutations rather than doing all possible (and this tells me if I need to increase the number of permutations to be sure my p-value is precise enough). With all possible permutations, there is no sampling, and no need for an interval, the p-value is exact. Thanks again, I need to remember combn.
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