[R] [OT] "plot y against x"

[Charles Annis, P.E.]

Engineers have been plotting stress (or strain, or log of either) as y
against log(fatigue lifetime) as x for 100 years or more.  Thus it appears
that allowable stress is a function of required cycles, and that is how the
plot is interpreted.  The underlying regression, however, correctly treats
observed lifetime as the dependent variable (even though it's plotted as x)
and testing stress (or strain, in a strain-controlled test) as the
independent variable (plotted as y).  Errors are in the horizontal
direction.  The curve is just "plotted wrong."  However, the convention of
plotting stress (or strain) vertically and lifetime horizontally is so
universal among engineers, that a statistician risks loss of credibility to
present a curve with the axes exchanged, even though both plots have the
identical underlying regression.  

Charles Annis, P.E.
 
Charles.Annis at StatisticalEngineering.com
phone: 561-352-9699
eFax:  503-217-5849
http://www.StatisticalEngineering.com

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Ted Harding
Sent: Monday, May 31, 2004 10:52 AM
To: r-help at stat.math.ethz.ch
Subject: [R] [OT] "plot y against x"

Hi Folks,

I'd be grateful for some views on the following.

When I say "plot y against x" I mean that y is on the vertical
axis and x is on the horizontal axis. I acquired this usage so
long ago that I can no longer remember how I acquired it, and
therefore can not cite my "authority" for my usage. There can
also be an implication that y is a function of x (or y is a
"dependent" variable and x an "independent" variable).
To the best of my knowledge, this is the standard usage.

However, I have had a query which suggests that the "transposed"
meaning may be quite frequently adopted, i.e.

  "plot x [horizontal axis] against y [vertical axis]"

Google tells me that "plot y against x" throws up about 147 hits,
while "plot x against y" throws up about 54 hits. One of the
latter is unequivocal and comes from a respected department of
mathematics:

http://www.maths.lancs.ac.uk/dept/coursenotes/lab100/pdffiles/a12.pdf

  Q 12.1 A simple plot.
  Invoke Matlab in an Xterm window and position the
  Figure window so that you can see it properly.
  x = -3:5    % plotting values (range)
  y = 2*x + 3 % a linear function of x
  plot(x,y)   % plot x against y

and at least two refer to "Statistical analysis with R" (so maybe
I'm not so off-topic after all), also unequivocal, e.g.:

http://www.nbn.ac.za/Education/11-stats-2004/R1.8/r_workshop.pdf 

  Example: Plotting functions
  Assume that you were to plot a function by hand. One possibility
  of doing it is to
  1. Select some xvalues from the range to be plotted
  2. Compute the corresponding y = f(x) values
  3. Plot x against y
  4. Add a (more or less) smooth line connecting the (x; y)points
  ...
  plot(x, y)            # plots x against y

(However, in R itself, "?plot" is discretely silent about what is
 "against" what!)

I'd value commments on whether the above "transposed" usage is in
fact sufficiently common (perhaps mainly in certain subject areas)
as to constitute a "linguistic enclave" with a valid dialectal
usage which is the opposite of the standard. Or maybe there isn't
really a standard.

This would help to respond to the query, which whether in writing
something which uses "plot y against x" it would be worth while
including an explicit explanation of which way round it is meant,
so that it's clear to any reader, whichever dialectal group they
belong to.

There was also a related query on whether "regression of Y on X"
could be understood the "wrong way round" and about usage of the
phrase "a model for Y against X". Where regression is concerned,
I don't think there is room for doubt and anyone who interpreted
it on the lines of "X~Y" is simply wrong. "Model for Y against X",
however, is not a standard phrase, I think (though clear enough
if you make the analogy with "plot"), and would need the same
disambiguation as "plot y against x" (if any is needed).

With thanks!
Best wishes to all,
Ted.


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 31-May-04                                       Time: 15:51:53
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