R help - Sep 2000 - qqnorm(), is it "backwards"?

Hello R friends,

I'm wondering why I get funny qqnorm() results.  It seems that they should
all be reflected in the normal qqline().

For instance: if I qqnorm() bimodal or uniform data I get a sigmoidal in
which the qqnorm() points lie above the qqline() at -ve theoretical
quantiles, and the qqnorm() points lie below the qqline() at +ve
theoretical quantiles.  Yet I expect such platykurtic distributions to go
the other way (eg pg 117 in _Biometry_  Sokal & Rohlf, 3rd ed).

The same thing with skewed data, I expect right skewed data to show a
negatively accelerating shape, but qqnorm() curves upwards.

Am I missing something, or is qqnorm() consistently heading in the wrong
diirection?

Cheers,
-P.

-- 
Peter L. Hurd, Ph.D.
phurd at uts.cc.utexas.edu
http://www.zo.utexas.edu/research/phurd                 fax 512.471-3878
Section of Integrative Biology, University of Texas, Austin TX 78712 USA


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At 17:10 21/09/00 -0500, Pete Hurd wrote:
>Hello R friends,
>
>I'm wondering why I get funny qqnorm() results.  It seems that they
should
>all be reflected in the normal qqline().
>
>For instance: if I qqnorm() bimodal or uniform data I get a sigmoidal in
>which the qqnorm() points lie above the qqline() at -ve theoretical
>quantiles, and the qqnorm() points lie below the qqline() at +ve
>theoretical quantiles.  Yet I expect such platykurtic distributions to go
>the other way (eg pg 117 in _Biometry_  Sokal & Rohlf, 3rd ed).
>
>The same thing with skewed data, I expect right skewed data to show a
>negatively accelerating shape, but qqnorm() curves upwards.
>
>Am I missing something, or is qqnorm() consistently heading in the wrong
>direction?
Yes, you are missing something.

Sokal and Rohlf do their normal scores plots the *wrong* way round and put
the rankits (or normal scores) on the y-axis and the observations on the
x-axis.  To its credit R and S-PLUS get it *right* by default and put the
independent variable (normal scores) on the x-axis and the dependent
variable (observations, residuals, ...) on the y-axis.

Sokal and Rohlf are not alone in their *error*, of course.  Minitab also
*messes* it up like this, for example.  I have no idea where this absolute
*heresy* comes from, but someone really ought to do some serious
extermination of this pernicious silliness before it goes too far...  

:-)

Bill Venables.
--
Bill Venables, Statistician                         Tel. +61 7 3826 7251 
CSIRO Marine Laboratories,                          Fax. +61 7 3826 7304
Cleveland, Qld, 4163                  Email: Bill.Venables at cmis.csiro.au
AUSTRALIA                        http://www.cmis.csiro.au/bill.venables/


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On Thu, 21 Sep 2000 17:10:27 -0500 (CDT), Pete Hurd
<phurd at uts.cc.utexas.edu> wrote:
>Hello R friends,
>
>I'm wondering why I get funny qqnorm() results.  It seems that they
should
>all be reflected in the normal qqline().
I think the problem is that there are several different conventions
for drawing these.  Some people put the theoretical quantiles on the x
axis (like R does), some put them on the y axis.  I think some people
plot probabilities rather than quantiles.  Some books (e.g. if I
recall correctly, Montgomery and Peck's regression text) even label
things one way and draw them another.

As far as I can tell, R is doing things correctly according to the
convention it uses.  That convention makes sense to me, too:  like all
plots of residuals, the residuals are shown on the y axis, the "fixed
things" on the x axis.

For a sample like runif(1000), the plot curves up at the left and down
at the right, because the uniform distribution doesn't take such
extreme values as the normal distribution does.

Duncan Murdoch
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