[R] Plotting positions in qqnorm?

David Scott d.scott at auckland.ac.nz
Fri Apr 14 13:49:05 CEST 2006

On Thu, 13 Apr 2006, Spencer Graves wrote:

> 	  Do you know of a reference that discusses alternative choices for
> plotting positions for a normal probability plot?  The documentation for
> qqnorm says it calls ppoints, which returns qnorm((1:m-a)/(m+1-2*a))
> with "a" = ifelse(n<=10, 3/8, 1/2)?  The help pages for qqnorm and
> ppoints just refer to Becker, Chambers and Wilks (1988) The New S
> Language (Wadsworth & Brooks/Cole), and I couldn't find any discussion
> of this.
> 	  I seem to recall that this was discussed in 1960 or earlier in a
> paper by Anscombe, but I can't find a reference and I wonder if someone
> might suggest something else.  I've been asked to comment on specialized
> software that allows the user to select "a" = +/-0.5, 0, 0.3, and 0.3175
> (but not 0.375 = 3/8, curiously).
> 	  I'd also be interested in any examples of real data sets where the
> choice of "a" actually made a difference.  When I've had so few data
> points that the choice for "a" might make a difference, a normal
> probability plot was not very informative, anyway, and I get more
> information from a simple dot plot.  If your experience is different,
> I'd like to know.
> 	  Thanks,
> 	  Spencer Graves
I suspect that what you are looking for is this paper:

Hyndman, Rob J. and Fan, Yanan (1996)
Sample quantiles in statistical packages
The American Statistician, 50, 361-365

which discusses different definitions of sample quantiles. See also the 
documentation for quantile.

David Scott
David Scott	Department of Statistics, Tamaki Campus
 		The University of Auckland, PB 92019
 		Auckland	NEW ZEALAND
Phone: +64 9 373 7599 ext 86830		Fax: +64 9 373 7000
Email:	d.scott at auckland.ac.nz

Graduate Officer, Department of Statistics

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