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st: Folding a density to check for symmetry or examine skewness
Here is something simple that may amuse -- or even be
useful in teaching or data exploration.
A symmetric distribution has identical left and right
parts, either side of its middle. In the case of a unimodal
distribution that middle will also be its mode, median and
A skewed distribution will have different left and right parts,
no matter what "middle" you select. This is a matter of definition,
but checking that this is so or examining asymmetry in detail
can be worthwhile.
We can fold to superimpose the two parts:
. u auto, clear
(1978 Automobile Data)
. kdensity mpg, gen(density) at(mpg)
Pick a "middle", in this case a mode at 19:
. gen distance = abs(mpg - 19)
. label var distance "distance from mode (mpg)"
. gen label = cond(mpg > 19, "R", cond(mpg < 19, "L", "M"))
. scatter density distance, mla(label) ms(i)
In a right-skewed distribution, the "R" points are higher,
and so forth.
I tried labels of "+" and "-" as well, but that is
not so good. The minus sign is too small. (The underscore "_"
would be placed too low.)
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