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