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QQ plot x-axis values

To: s-news@lists.biostat.wustl.edu
Subject: QQ plot x-axis values
From: Paul Matthias Diderichsen <paulmatthias.diderichsen@abbott.com>
Date: Tue, 10 Oct 2006 15:40:12 +0200

Dear S-plus users.
I learned more or less all I know about Q-Q plots by reading http://en.wikipedia.org/wiki/Qq_plot and related ressources on the web. I think that I now understand more or less how these beasts work.

Of course, there's still one issue: There seems to be a discrepancy between what wikipedia says and what S-plus does.

> a<-data.frame(NORM=rnorm(3))
# a$NORM could be any 3 values since I'm only interested in x below...
> qqmath(~NORM,data="">
[1] -0.9674216  0.0000000  0.9674216
> qnorm(c(1/6,3/6,5/6))
[1] -0.9674216  0.0000000  0.9674216

versus: "k/(n + 1)-quantiles of the comparison distributon (e.g. the normal distribution) on the horizontal axis (for k = 1, ..., n)"

In the example above, I create a qqplot with three points. As I understand wikipedia, these should be (on the x-axis) at the 1/4, 2/4, and 3/4 quantiles of the normal distribution. However, instead they are at the 1/6, 3/6, and 5/6 quantiles.

I'd appreciate it a lot, if anybody can explain to me what is "right". (Of course: Gurus - feel free to correct/add to the wikipedia entry in case it's not accurate!)

Kind regards and TIA - PMD.
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