Re: off-by-one in boxplot?

[sfeam (E. Merritt) <eam...@gm...>]

On Monday, 02 May 2011, Allin Cottrell wrote:
> I'm wondering if there might be an off-by-one bug in gnuplot's
> built-in boxplot functionality.
> 
> I'm attaching a small data file which I've tried plotting using
> the following commands (simplified from boxplot.dem):
> 
> set style data boxplot
> set pointsize 0.5
> set border 2
> set xtics ("wage" 1) scale 0.0
> set xtics nomirror
> set ytics nomirror
> plot 'wage.dat' using (1):1 notitle
> 
> I calculate quartiles 1 and 3 as 1345 and 2140, respectively, and
> this seems to agree with what gnuplot shows for the central box. I
> therefore get 795 for the inter-quartile range, and multiplying
> this by the default range multiplier of 1.5 I get 1192.5. Adding
> this to Q3 gives 3332.5 for the upper whisker limit. The greatest
> y-value in the data less than or equal to 3332.5 is 3307, so I'd
> expect the upper whisker to extend that far, but it extends only
> to about 2600, which could correspond to the next largest y-value,
> namely 2613.
> 
> That is, I think that according to the docs one should see a
> whisker extending to 3307 and three high outliers, but in fact I
> see the whisker going to about 2600 and four high outliers. I can
> get the result I'd expect to see with the default "range" value of
> 1.5, if I do
> 
> set style boxplot range 1.6

1st quartile == smallest index that encompasses 1/4 of the data points
              = data[ceil(49/4)] 
              = 1433

3rd quartile == smallest index that encompasses 3/4 of the data points
              = data[ceil(49*3/4)] 
              = 2115

1.5 * inter-quartile difference = (2115-1433) * 1.5 = 716.1

" The most distant point whose value lies within" 716.1 of 2115 is
2613, which is where the whisker ends.

There are surprisingly many differing definitions of "quartile".
I can sympathize if you prefer a different one than gnuplot uses,
but I think gnuplot is at least consistent with its own definition.

If people care enough about the definition of "quartile", I suppose we
could offer configuration options that select from a set of possible
definitions.  R does this, as I recall.
 
	Ethan