On Thu, 26 Mar 2009, Jason Rupert wrote:
The R code below produces (after running for a few minutes on a decent
computer) the plot shown at the following location:
http://n2.nabble.com/Is-there-a-physical-and-quantitative-explanation-for-this-plot--td2542321.html
I'm just taking the mean of a given set of random variables, where the set size
is increased. There appears to be a quick convergence and then a pretty steady
variance out to a set size of 10,0000.
Part of the convergence is just that the standard devation of a mean of N
observations is proportional to 1/sqrt(N). In your case the distributions are
all exactly Normal; the same convergence would occur with other distributions,
but you would also see the change in shape from left to right as the
distribution converged to Normal.
There's also some plotting artifacts due to the size of the points. The
apparent stabilization at large N (and the wide vertical bar at zero that Marc
Schwartz commented on) are due partly to the slow convergence of 1/sqrt(N) but
largely because the width can't be smaller than the width of a point.
When I draw funnel plots like this for whole-genome association data I use the
'hexbin' package, which doesn't have these artifacts and is much faster and
produces smaller graphics files.
-thomas
Thomas Lumley Assoc. Professor, Biostatistics
tlum...@u.washington.edu University of Washington, Seattle
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