Date: Mar 10, 2013 11:52 AM
Author: Luis A. Afonso
Subject: Permutations, different aims

Permutations, different aims

They are in use yet indexes
specifying what item from a sample is chosen. So needles to rename the ones indicative the time j an item is randomly drawn among the sample set. We use the fact that with W(j)= j/(0.5 * n * (1+n)) and X´ an item randomly and exhaustively chosen,
___mmX=(1<=j<=n)SUM X´(random)*W(j)
has as Mathematical Expectation the sample mean value: E(mmX)=m.
Deriving from the way the permutations are performed there are important differences between the classical Fisher´s Permutation Test (FP) and the Intra-Permutation one (IP) in what concerns the Two Sample Difference on Means. Recall that FP respects all items whatever the sample and the result is a Confidence Interval (CI) providing the bounds when they are merely insignificant/confounding, whereas IP which the permutation among items are restricted to the respective sample one can get the bounds of the wanted difference and conclude that it was no significant, 0 is inside the interval, or on contrary significant: 0 is outside. By other words: if is a NHST or a No-Null Hypotheses Statistical Test.
Luis A. Afonso