Re: st: RE: Histograms (was: Multiple (overlaid) Histogram)

[Marcello Pagano <pagano@hsph.harvard.edu>]

As I have said before, I would very much like, with Allan Reese, an 
option for equi-probability histograms.  I think that this is especially 
useful when thinking of the histogram as an estimator of an underlying 
density function of a continuous variable. I do not see a strong 
argument, other than tradition (laziness?), for being constrained to 
histograms with equi-spaced bins.

m.p.



Nick Cox wrote:

> R. Allan Reese
>
>
> > On Thu, 29 May 2003, Nick Cox wrote:
> >
> > > ... Empirical. You will see histograms with unequal widths
> > > particularly in older books and papers, and the reason was
> > > that data for them came already grouped in such classes. There's
> > > an example in Snedecor and Cochran's venerable text.
> > > That seems far less common today when more and more data sets are
> > > available in raw, ungrouped form, modulo confidentiality
> > > constraints. I don't see people asking for this often on
> > Statalist,
> >
> > > and one good reason for this being low down in priority is that
> > > it is practice rarely needed.
> > The linked issue is whether it is strictly true, as Nick previously
> > commented, that "adjacent bars touch. (If this isn't true,
> > you haven't got
> > a proper histogram.)"  In a histogram, it is unit area that
> > represents the
> > weight of data.  Hence a class interval that is widened should be
> > proportionately reduced in height.
> >
> > I suggest this is a "design decision" which has implications for the
> > message conveyed by a graph.  Consider a data series such as
> > 4,4,4,5,5,5,5,5,6,6,6,6,16 and use for convenience unit-width bins.
> > Stata's histogram command shows the 16 as a single observation and,
> > implicitly, as an outlier.  If you don't allow zero-height
> > bars but demand
> > that adjacent bars touch, the upper bin might run from 7 to
> > 16 with a
> > height of 0.11 and the data now look like a skewed
> > distribution with a
> > long upper tail.  Neither version is more "correct"
> > absolutely, though one
> > may be more appropriate to an interpretation of the data.
> >
> > Hence, I would support adding the option in the software,
> > eg a new option
> > "classes(4,5,6,7,16)" or "width(1,1,1,9)", to allow
> > irregular spacing.
> > The user then has control of the design choice, rather than being
> > compelled by the software (writer).
> >
> > Excel has particularly abhorrent approaches to the choice
> > and labelling of
> > bins for histograms.
>
> As for the definition, I am more than happy with the idea that some
> bars are of zero height and touch other bars which may be of zero
> or non-zero height. That is, my definition emphatically does not
> rule out gaps between bars: they are just populated by bars of
> zero height. (Or, if you like, the principle that adjacent bars
> touch does not rule out the possibility of bars not being adjacent.)
>
> As for an extra option, it is easy to specify this as a desired item,
> but my guess is that implementing this on top of the
> existing -histogram-
> command would be far more of a labour than the real benefits
> imply. That's Stata Corp's problem, but it could be enough
> to push this a long way down the list of priorities.
>
> In addition, I doubt that all users have as much graphical sense
> as Allan. This option could be a gateway to lots of rather silly
> histograms, and although one shouldn't rule out syntax on the
> grounds that it might be abused, I feel queasy at the prospect.
>
> Nick
> n.j.cox@durham.ac.uk
>
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--
______________________________________________________________________

Marcello Pagano
Biostatistics Department			Tel: 1-617-432-4911
Harvard School of Public Health		        Fax: 1-617-739-1781
655 Huntington Avenue            		email:pagano@biostat.harvard.edu
Boston, MA  02115                 		http://biosun1.harvard.edu/~bio200
USA

eppur si muove


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