Paired permuted t-tests?

Question

I have a small dataset which are not normally distributed. I would like to perform a pairwise analysis of the differences in values between two groups. It has been suggested that I use permuted t-tests to perform this analysis, as this gets around the problem of normality assumption.

Since I need to perform a paired samples analysis, I have been digging around for a function in R that will allow me to specify this. I have come across perm.test() in the exactRankTests package (link). This allows me to pass a paired = TRUE argument, so I assume this is what I'm looking for - that it performs a permuted, paired, t-test.

I have two questions:

1. Is the concept of a paired permuted statistical test nonsense? My understanding, until now, was that you can only permute in non-paired data, but maybe I'm wrong - I'm not too experienced in stats.
2. Am I right to assume that the function I have chosen is doing the right thing? Running it on my data, it certainly looks like it comes to the right conclusions... But I'd like to be confident before publishing anything based on the values provided by this obscure R package.

Answer 1

It makes perfect sense to have a permutation test on paired data:

The first is that the test would be performed on the differences, and randomly permuting the order in the differences (i.e. permuting the group labels within the pair) is equivalent to attaching a random sign to the absolute difference. (A Wilcoxon signed rank test -- that's actually a paired-permutation test performed on ranks of differences)

(I would suppose that's what the paired argument is taking care of, but I'm unfamiliar with the package.)

The assumption for exchangeability under the null would be similar to the signed rank test (of symmetry of differences).