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st: Y axis values for hist ,density

From   "Allan Reese (Cefas)" <>
To   <>
Subject   st: Y axis values for hist ,density
Date   Thu, 27 Oct 2005 14:02:45 +0100

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

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