Date: Feb 6, 2013 3:53 AM
Author: Luis A. Afonso
Subject: Re: Intra-permutations to test two different mean values

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From the Distribution X~N(0,1):n it was lead to compare with Y~N(m,s):n such that with samples sizes k=7, 10, 15:
____________1) Y~N(5,2)
____________2) Y~N(10,3)
____________3) Y~N(15,5)
____________4) Y~N(20,10)
Resulting the following 2 tails 5% and 1% significance level Confidence Intervals, (fractiles 0.025, 0.975, 0.005, 0.995) considering 400ยด000 values each case, for the r.v. mmE(Y - X), Intra-Permutations:
______________n=7_________10__________15____________
_N(5,2)_____[3.13, 6.86]___[3.43, 6.57]___[3.71, 6.29]___5%___
___________[2.51, 7.49]___[2.90, 7.09]___[3.30, 6.70]___1%___
_N(10,3)____[7.37, 12.63]__[7.79, 12.21]__[8.18, 11.82]__
___________ [6.50, 13.50]__[7.06, 12.94]__[7.61, 12.39]__
_N(15,5)____[10.76, 19.22]_[11.43, 18.56]_[12.08, 17.95]_
___________ [9.40, 20.59]__[10.27, 19.71]_[11.15, 18.83]_
_N(20,10)___ [11.66, 28.33]_[12.98, 27.02]_[14.24, 25.80]_
___________ [9.02, 31.00]__[10.69, 29.26]_[12.41, 27.57]_
Conclusion/Extension
Because E(W) = E(mmW) one can eventually induce a way to test whatever function G(E(X), E(Y)) by this method was gotten.
Luis A. Afonso