Date: Feb 3, 2013 6:50 PM
Author: Luis A. Afonso
Subject: Re: Intra-permutations to test two different mean values

Follow-up: A case study

Data is that presented at my Feb. 27, 2005 8:16 AM concerning skull´s length of extinct jackals by sex. Manly. B. F. J. (1991) Monte Carlo Methods in Biology. Chapman & all.
Males: 120, 107, 110, 116, 114, 111, 113, 117, 114, 112.
Females: 110, 111, 107, 108, 110, 105, 107, 106, 111, 111.
_X___mean= 113.4 mm, sd= 3.718
_Y_________108.6 , 2.271
_obsv. diff= 4.8___ Normal Model, T= 3.484164, p-value= .0013.
Note that because the 5% significance level, 2 tails critical value (18df) is -2.1009 we conclude that [5.275, 8.325] contains the observed difference of Population means with 95% confidence.
A- Fisher´s Permutation (alpha=5% , 1% approx.)
___[-3.4 (.026), 3.4 (.981)] --- > 4.8 outside
___[-4.2 (.007), 4.2 (.996)]
B- Intra-Permutation
___[3.4 (.030), 6.2 (.979)] --- > 4.8 inside, interval centre.
___[3.1 (.007), 6.5 (.996)]
The main fact to retain from these calculations is that one can safely disregard the normal model and use permutation methods even that there are sufficient evidence of no homogeneity in variances regarding the Populations.
Note
___The Fisher´s Permutation test is used when we intend to find if the null hypotheses is valid (equal variances), on contrary the Intra-Permutation is designed to find out confidence intervals concerning differences of Population means, I guess . . .

Luis A. Afonso