Hi Maurizio,

I’ve not used this particular test before but the basic idea is familiar to me; and I’m basing my reply also on a simplified description of the test in Chapter 1 of Jun S Liu’s (excellent) book “Monte Carlo Strategies in Scientific Computing”.

So the basic idea behind the permutation test proposed by Efron & Petrosian is to test the null hypothesis that the two random variables are independent by comparing a given test statistic of the observed data against the distribution of that test statistic expected in the long run under the null hypothesis.  It’s not a Bayesian analysis so we don’t begin with any strong assumptions as to the distributional shapes of the two random variables; instead we will use our observed data under  possible permutations of x’s with y’s as a proxy for this null distribution.  If there was no truncations of the data points then the standard permutation test we can compute the null distribution of the test statistic from simple (uniform) random permutation of the x’s with y’s (this is the independence assumption of the null).  But since we have these truncations in our observed data we must make sure our permutations also satisfy the same conditions as the observed data, whilst maintaining the uniformity of the permutation process: this part is the ‘trick’ of the Efron & Petrosian algorithm.  After defining this permutation process and choosing the optimal test statistic (see the discussion in Efron & Petrosian) the final details are just those of standard frequentist hypothesis testing with p-values.

Hope that helps,

Ewan.