Dear Greg,
thank you for your reply - that is very helpful!
regards
Avril
"Greg Snow" <Greg.Snow@intermountainmail.org> wrote: 
> As an alternative you could try quantile regression (find a regression
> line for the 95th percentile), if the relationship between max(y) and x
> is only due to more points (and therefore more oportunities for large
> values) then the estimated quantile lines should not differ
> significantly from 0.
> 
> Try the following (where the truth is no relationship):
> 
> set.seed(2)
> 
> x <- rep(1:10, 1:10)
> y <- rexp(55, 1)
> 
> plot(x,y)
> 
> cor.test( 1:10, tapply( y, x, max ) )
> 
> library(quantreg)
> fit <- rq( y ~ x, tau=c(0.5, 0.95) )
> summary(fit)
> 
> 
> Notice that the cor.test is significant, but that the confidence
> intervals for the slopes both include 0.
> 
> Hope this helps,
> 
> -- 
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow@intermountainmail.org
> (801) 408-8111
>  
>  
> 
> > -----Original Message-----
> > From: r-help-bounces@r-project.org 
> > [mailto:r-help-bounces@r-project.org] On Behalf Of Avril Coghlan
> > Sent: Thursday, November 22, 2007 5:46 AM
> > To: r-help@stat.math.ethz.ch
> > Cc: alc@sanger.ac.uk
> > Subject: [R] question about extreme value distribution
> > 
> > Hello,
> > 
> > I have a question about using extreme
> > value distribution in R. 
> > 
> > I have two variables, X and Y, and have pairs of points 
> > (X1,Y1),(X2,Y2), (X3,Y3) etc.
> > When I plot X against Y, it looks
> > like the maximum value of Y (for a particular X) is correlated with X.
> > 
> > Indeed, when I bin the data by X-value into equally sized 
> > bins, and test whether the maximum value of Y for a bin is 
> > correlated with the mean X for the bin, there is a 
> > significant correlation between max(Y) and X. However, I am 
> > not very happy with this because there is not an equal number 
> > of data points in each bin.
> > 
> > I imagine that there is a better statistical test that I 
> > could use, if I could fit an extreme value distribution to the Y data.
> > However, I'm not sure how to do this. 
> > I am wondering is there a way to use the extreme value 
> > distribution functions in R to test the hypothesis that the 
> > maximum of Y (for a particular X) is correlated with X?
> > 
> > I would appreciate advice very much.
> > 
> > regards
> > Avril Coghlan
> > 
> > 
> > 
> > 
> > 
> > 
> > 
> > --
> >  The Wellcome Trust Sanger Institute is operated by Genome 
> > Research  Limited, a charity registered in England with 
> > number 1021457 and a  company registered in England with 
> > number 2742969, whose registered  office is 215 Euston Road, 
> > London, NW1 2BE.
> > 
> > ______________________________________________
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> > PLEASE do read the posting guide 
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> > 
> 

