[R] regression towards the mean, AS paper November 2007

Troels Ring tring at gvdnet.dk
Mon Dec 17 19:21:39 CET 2007

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

Sigma <- matrix(c(1,0.7,0.7,1),2,2)
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 - -
tring at gvdnet.dk

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