R devel - Jul 2009 - box and whisker (PR#13821)

In a Box and Whisker plot, I thought that when there are outliers both above and
below the whiskers, then the whiskers should both be the same length (plus or
minus 1.5 times the inter-quartile range).

If you look at the plot for SilwoodWeather on p.155 of The R Book you will see
that for November (month =3D 11) the upper whisker is shorter than the lower,
while for other months with outliers both above and below, the lines are the
same lengths.

When there are no outliers, then of course the maximum and minimum values result
in whiskers of different lengths above and below.

Here is the code that creates the problem:

data<-read.table("c:\\temp\\SilwoodWeather.txt",header=3DT)
attach(data)
names(data)

[1] "upper" "lower" "rain"  "month"
"yr"

month<-factor(month)
plot(month,upper)

and exactly the same with

boxplot(upper~month)



Best wishes,

Mick

Prof  M.J. Crawley  FRS

Imperial College London
Silwood Park
Ascot
Berks
SL5 7PY
UK

Phone (0) 207 5942 216
Fax     (0) 207 5942 339


	[[alternative HTML version deleted]]

m.crawley at imperial.ac.uk wrote:
> In a Box and Whisker plot, I thought that when there are outliers both
abov> e and below the whiskers, then the whiskers should both be the same
length > (plus or minus 1.5 times the inter-quartile range).
Not according to the docs:

    range: this determines how far the plot whiskers extend out from the
           box.  If 'range' is positive, the whiskers extend to the most
           extreme data point which is no more than 'range' times the
           interquartile range from the box. A value of zero causes the
           whiskers to extend to the data extremes.

And the code itself has

             stats[c(1, 5)] <- range(x[!out], na.rm = TRUE)

So the whisker won't be equal to 1.5 IQR unless there happens to be an 
observation there.

Now, this might be wrong, but people have tried very hard to make the 
implementation follow the original definition due to Tukey. I.e., if you 
can point out that Tukey specified it otherwise, then we'd change it, 
otherwise it is just not a bug.
> If you look at the plot for SilwoodWeather on p.155 of The R Book you will
> see that for November (month =3D 11) the upper whisker is shorter than the
> lower, while for other months with outliers both above and below, the
lines>  are the same lengths.
For easier reproduction (reproducible examples should not refer to files 
on your C: drive...):

 > diff(boxplot({set.seed(9);x<-rnorm(50)})$stats)
           [,1]
[1,] 1.2525857
[2,] 0.5412128
[3,] 0.6083348
[4,] 1.4625057



-- 
    O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

>>>>> "PD" == Peter Dalgaard <p.dalgaard at
biostat.ku.dk>
>>>>>     on Sun, 12 Jul 2009 11:11:37 +0200 writes:
    PD> m.crawley at imperial.ac.uk wrote:
    >> In a Box and Whisker plot, I thought that when there are outliers
both abov    >> e and below the whiskers, then the whiskers should both be
the same length     >> (plus or minus 1.5 times the inter-quartile range).

    PD> Not according to the docs:

    PD> range: this determines how far the plot whiskers extend out from the
    PD> box.  If 'range' is positive, the whiskers extend to the most
    PD> extreme data point which is no more than 'range' times the
    PD> interquartile range from the box. A value of zero causes the
    PD> whiskers to extend to the data extremes.

    PD> And the code itself has

    PD> stats[c(1, 5)] <- range(x[!out], na.rm = TRUE)

    PD> So the whisker won't be equal to 1.5 IQR unless there happens to
be an
    PD> observation there.

    PD> Now, this might be wrong, but people have tried very hard to make the
    PD> implementation follow the original definition due to Tukey. I.e., if
you
    PD> can point out that Tukey specified it otherwise, then we'd change
it,
    PD> otherwise it is just not a bug.

I'd bet pretty large amounts that we (and S and S-plus probably
quite few otherpackages) have implemented the whiskers the way
JWT defined them, very purposefully.

One of JWT's point *was* exactly that most of the values "drawn"
represent *observations* (and those that do not use
exact mid points of obs.):
It's not by coincidence or even queerness that the box is *not*
delineated by the usual quartiles, but rather the *hinges*

[ Digression about hinges vs quartiles : 

   ?boxplot.stats

  has a section 'Details'  to which I had added such information about
  decade ago.
  Whereas our R help pages ( ?boxplot.stats,  ?fivenum ) 
  do use the correct definitions,
  unfortunately many other places do *not*, e.g., even the
  Wikipedia page  http://en.wikipedia.org/wiki/Five-number_summary
  wrongly talks about 1st and 3rd quartile,
  but then at least uses a numerical example using the hinges
]

Martin Maechler, ETH Zurich

    >> If you look at the plot for SilwoodWeather on p.155 of The R Book
you will     >> see that for November (month =3D 11) the upper whisker is
shorter than the     >> lower, while for other months with outliers both
above and below, the lines    >> are the same lengths.

    PD> For easier reproduction (reproducible examples should not refer to
files
    PD> on your C: drive...):

    >> diff(boxplot({set.seed(9);x<-rnorm(50)})$stats)
    PD> [,1]
    PD> [1,] 1.2525857
    PD> [2,] 0.5412128
    PD> [3,] 0.6083348
    PD> [4,] 1.4625057



    PD> -- 
    PD> O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
    PD> c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
    PD> (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45)
35327918
    PD> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45)
35327907

    PD> ______________________________________________
    PD> R-devel at r-project.org mailing list
    PD> https://stat.ethz.ch/mailman/listinfo/r-devel