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st: quantile-quantile plots

From   Nick Cox <>
To   "" <>
Subject   st: quantile-quantile plots
Date   Mon, 15 Apr 2013 11:21:12 +0100

Some recent threads have mentioned quantile-quantile plots. Q-Q plots
go back to the nineteenth century in the specific case of so-called
normal probability plots (really observed quantiles versus expected
normal quantiles, or vice versa,  depending on what one means by

The key paper mentioned by David Hoaglin

Wilk MB, Gnanadesikan R. 1968. Probability plotting methods for the
analysis of data.  Biometrika 55:1-17.

is over 40 years old, but the idea is still not yet anywhere as widely
practised as it should be. By the way, that is a spectacular paper,
which pays re-reading every few years.

I want to push a few related hints that might otherwise be buried in
those threads, which people interested in this topic might well not be

First off, and most obviously, Stata has long had a -qqplot- command.

However, it assumes that you want to compare two variables. If not,
-cquantile-  (SSC) is a helper command that gets you to that

Quantile-quantile plots are for comparing two distributions. If you
have several, then -qplot- (SJ) allows overlay, or display

If you want yet more ideas in the same vein, check out

SJ-7-2  gr0027  . .  Stata tip 47: Quantile-quantile plots without programming
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        Q2/07   SJ 7(2):275--279                                 (no commands)
        tip on producing various quantile-quantile (Q-Q) plots

free .pdf


* A note on "versus" or "against". I was brought up -- probably in
school physics, but it was last century, so I can't give precise
recollections -- to say "plot y versus x" where y is, not
surprisingly, whatever is plotted on the y or vertical axis. That
seems to me to match mathematics and physics usages such as y is a
function of x, or output is a function of time, where the dependent
variable (outcome, response) is always mentioned first. But I've come
across people saying "plot x versus y". If anyone has a logic for that
usage, I'd be interested to hear it.
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