[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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