Luis A. Afonso
Posts:
4,530
From:
LIsbon (Portugal)
Registered:
2/16/05


Re: Intrapermutations to test two different mean values
Posted:
Feb 14, 2013 4:50 PM


Deception and joy. . .
The only motivation leading me to try to find out a algorithm able to *multiply* data was the repugnance to concede, in spite of fully used nowadays by Statisticians, that Bootstrapping is a illogic method to do it. In fact to repeat items at a sample, furthermore with no control how much are they, seems to me implausible or odd. So a modified mean, mm, was defined as the sum of the products of the items by l(j) = j/(1+2+?+n) : mm= sum (l(i)*x( )) where x( ) is a randomly item chosen without replacement among the n sample items exhaustively. In terms of expectation is E(mm)= sample mean. I was persuaded, till today, an improvement was found. Surprisingly Bootstrap and this IntraPermutation method when applied to evaluate Confidence Intervals for the difference of two sample means leads to the same results . . . ___95% and 99% C.I. (fractiles .025, .975 and .005, .995) samples regarding the difference of mean values of 30 females and 30 males of a spider´s species____(1´000´000 replications) ___Intrapermutations______ ___[1.76, 2.67]__[1.63, 2.81] ___[1.76, 2.67]__[1.63, 2.81] ___[1.76, 2.67]__[1.63, 2.81] ___[1.76, 2.67]__[1.63, 2.81]
___Bootstrap______________ ___[1.747, 2.668]__[1.598, 2.810] ___[1.747, 2.668]__[1.598, 2.842] ___[1.747, 2.670]__[1.598, 2.812] ___[1.746, 2.668]__[1.598, 2.810]
This is deceptive conclusion in practical terms, but conceptually interesting. In fact, the method demands a very weak feature: the items obtained in each observed sample must be completely independent, i.i.d..
Luis A. Afonso

