[R] Plotting positions in qqnorm?

Berton Gunter gunter.berton at gene.com
Thu Apr 13 23:09:47 CEST 2006

```Spencer:

I seem to remember that Jim Filliben did some work on this. Try checking the
references in this:

J. J. Filliben (1975)
The Probability Plot Correlation Coefficient Test for Normality
Technometrics, Vol. 17, No. 1, pp. 111-117

My experience agrees with yours: if sample sizes are small enough for it to
make a difference, then sample sizes are too small to say much useful about
the distribution anyway. Heresy: I gave up using normal and half normal
plots for screening designs years ago, as they never told me more (nor less)
than dot plots.

Cheers,
Bert

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Spencer Graves
Sent: Thursday, April 13, 2006 1:21 PM
To: R help list
Subject: [R] Plotting positions in qqnorm?

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

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