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st: RE: Y axis values for hist ,density


From   "Jann Ben" <ben.jann@soz.gess.ethz.ch>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Y axis values for hist ,density
Date   Thu, 27 Oct 2005 15:12:13 +0200

Bang! I don't agree. The purpose of a histogram is to make 
visible the shape of a density. It is therefore natural to 
report the y-axis in terms of a density. 
ben

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Allan Reese (Cefas)
> Sent: Thursday, October 27, 2005 3:03 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Y axis values for hist ,density
> 
> 
> The default "hist x" command in Stata gives a Y axis labelled 
> a density.  I've never given it much attention until I saw 
> the scale went up to 2 on a plot.  Hold on, density functions 
> sum to 1 over the variable.
> 
> Further investigation and discussion with Statacorp 
> identified that the default tries to make the "area" of the 
> bars add up to 1.  If the number of bars changes, so does 
> their width and so does the Y labelling.  In my example, the 
> data were discrete, so increasing the number of intervals did 
> not change the plot except to add more zero-height columns 
> and hence make each column narrower.
> 
> hist x, bin(n)            therefore caused different Y 
> labelling with varying n
> hist x, xcale(xrange(0 n) did not affect the labelling, 
> though the bars got narrower with bigger n
> hist x, frac              and 
> hist x, discrete          both gave correct labelling, and 
> the sum of column heights was 1. 
> 
> Do other users think this is perverse behaviour, especially 
> as the default?  My take is that, when drawing a histogram, 
> the column width is taken as an arbitrary unit, not directly 
> related to the x-scale.  The implication is that you need to 
> scale the height only when there are mixed-width columns, but 
> would not label the Y axis in "freq/absolute-width" units.  
> Having "densities" that vary and are in such peculiar units 
> (1/locust in my example!) does not seem helpful.
> 
> Shoot me down
> Allan
> 
> 
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