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st: RE: RE: Y axis values for hist ,density


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Y axis values for hist ,density
Date   Mon, 31 Oct 2005 18:06:30 -0000

Given Allan's charming start, it seems churlish 
to dissent. 

But densities of continuous variables can have any 
non-negative value consistent with their integrating to 1
over their support. This is not a point for discussion: it 
is standard probability theory arising directly from 
integral calculus. A very clear example is embedded 
in the manuals, at [R] kdensity I think. It follows also 
from the definition that changing the binning can change 
the empirical densities shown. It would be alarming if this were 
not so. 

Nick 
n.j.cox@durham.ac.uk 

Allan Reese
 
> Nick Cox is right:
> Allan's complaining about perceived perversity, but I am not 
> clear what he 
> would regard as good behaviour. 
> 
> Jann Ben is also right, and missed my point:
>  
> 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. 
> -------------------------------------------------------------------
> 
> I can see this is a case of computers do what you tell them, 
> but I'm not happy with it.
> As was also pointed out, there are alternatives and I'm the 
> first to agree that users should
> look at and understand the graphs they draw.
> 
> But there seems something inherently wrong in calling a scale 
> "density" when it can have 
> values greater than 1.  Nor is it obvious to me what point 
> there is having a scale when the
> values may change with the number of bins.  I must remember 
> to add "frac" every time, like
> I add ylab(,angle(0)) as a reflex ;-)

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