Is the purpose of permutation test to test the null that several groups of samples come from the same distribution?
I found its steps are
The steps in a permutation-based computation of the significance level of a test statistic are as follows:
i) Choose a test statistic, eg. a t-score for a comparison of two groups,
ii) Compute the test statistic for the gene of interest,
iii) Permute the labels on samples at random, and re-compute the test statistic for the rearranged labels; repeat for a large number (perhaps 1,000) permutations, and finally,
iv) Compute the fraction of cases in which the test statistics from iii) exceed the real test statistic from ii).
What kinds of test statistic should one choose in the first step?
The example uses the t-score, which measures the difference between two groups. But it seems to me that any statistic will work, not necessarily measuring the difference between two groups. Is it correct?