[R] boxplot notches

[David James]

Prof Brian Ripley wrote:
> On Mon, 1 Mar 2004, Martin Maechler wrote:
> 
> > >>>>> "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...
> 
> It may be approximately correct for the width of a CI (and when I checked 
> it was only appproximately correct for a normal), but I would seriously 
> doubt if it were approximately correct for a significance level of 5%.
> Remember how fast the tails of the asymptotic normal distribution decay: a 
> 20% error turns 5% into 2%.
> 
> BTW, if there is a precise reference for this it would be good to add it
> to boxplot.stats.Rd, as the confidence limits are unexplained there.

@article{McGi:Tuke:Lars:1978,
author = {McGill, Robert and Tukey, John W. and Larsen, Wayne A.},
title = {Variations of {B}ox plots},
year = {1978},
journal = {The American Statistician},
volume = {32},
pages = {12--16},
keywords = {Exploratory data analysis; Graphics}
}

@book{Cham:Clev:Klei:Tuke:1983,
author = {Chambers, John M. and Cleveland, William S. and Kleiner, Beat
and Tukey, Paul A.},
title = {Graphical methods for data analysis},
year = {1983},
pages = {395},
publisher = {Wadsworth Publishing Co Inc}
}

> 
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
> 
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