[R] boxplot notches

[Martin Maechler]

>>>>> "TL" == Thomas Lumley <tlumley at u.washington.edu>
>>>>>     on Mon, 1 Mar 2004 09:54:48 -0800 (PST) writes:

    TL> On Mon, 1 Mar 2004, Christoph Scherber wrote:
    >> Dear list members,
    >> 
    >> Can anyone tell me how the notches in boxplot(Y~X,notch=T)  are
    >> calculated? What do these notches represent exactly? I´d suppose they
    >> are Conficence Intervals for the median, but I´ve also been told they
    >> might show Least Significant Difference (LSD) equivalents.

    TL> The help page says that 
    TL> " If the notches of two plots do not overlap then
    TL>   the medians are significantly different at the 5 percent level."

    TL> The only thing wrong with this is that it isn't true.
    TL> The code says that the notches are +/- 1.58 IQR/sqrt(n),
    TL> so I think the claimed confidence level holds only for
    TL> normal distribuitons with small amounts of contamination.

I think John Tukey's idea was that this formula (or just the fact of
using median and quartiles) is still often approximately correct
for quite a few kinds of moderate contaminations...

Martin Maechler <maechler at stat.math.ethz.ch>	http://stat.ethz.ch/~maechler/
Seminar fuer Statistik, ETH-Zentrum  LEO C16	Leonhardstr. 27
ETH (Federal Inst. Technology)	8092 Zurich	SWITZERLAND
phone: x-41-1-632-3408		fax: ...-1228			<><