Dear friends, regression towards the mean is interesting in medical circles, and a very recent paper (The American Statistician November 2007;61:302-307 by Krause and Pinheiro) treats it at length. An initial example specifies (p 303): "Consider the following example: we draw 100 samples from a bivariate Normal distribution with X0~N(0,1), X1~N(0,1) and cov(X0,X1)=0.7, We then calculate the p value for the null hypothesis that the means of X0 and X1 are equal, using a paired Student's t test. The procedure is repeated 1000 times, producing 1000 simulated p values. Because X0 and X1 have identical marginal distributions, the simulated p values behave like independent Uniform(0,1) random variables." This I did not understand, and simulating like shown below produced far from uniform (0,1) p values - but I fail to see how it is wrong. I contacted the authors of the paper but they did not answer. So, please, doesn´t the code below specify a bivariate N(0,1) with covariance 0.7? I get p values = 1 all over - not interesting, but how wrong? Best wishes Troels
library(MASS) Sigma <- matrix(c(1,0.7,0.7,1),2,2) Sigma res <- NULL for (i in 1:1000){ ff <-(mvrnorm(n=100, rep(0, 2), Sigma, empirical = TRUE)) res[i] <- t.test(ff[,1],ff[,2],paired=TRUE)$p.value} -- Troels Ring - - Department of nephrology - - Aalborg Hospital 9100 Aalborg, Denmark - - +45 99326629 - - [EMAIL PROTECTED] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.