Re: FW: SD or SE ?

[Rich Strauss]

Right, although the conventional 'formula' for the standard error of the 
standard deviation [s/sqrt(2N); Spiegel 1961] is said to hold only for 
sample sizes in the hundreds.  Another less well known expression involves 
both the 2nd and 4th moments of the data distribution and seems to hold for 
sample sizes as low as 50 or so.  But I've found via simulation that both 
jackknifed and bootstrapped estimates of the SE of the SD are pretty good 
even for sample sizes as low as 15-20, and so there's really no good reason 
not to present them in reporting the results of a data analysis.

At 12:19 PM 4/1/2003 -0500, you wrote:
At 11:43 AM 4/1/2003, Rich Strauss wrote:
The important point, I think, is that SDs and SEs measure two different 
things.  The standard deviation is a measure of variation within a 
sample, and is an estimate of the amount of variation in the population 
from which the sample was drawn.  The standard error is a measure of 
uncertainty (sampling variation) in some statistic, such as the sample 
mean, and is used to derive confidence intervals and such.  As sample 
size increases, the standard deviation converges (almost) on its "true" 
value, while the standard error converges on zero.
of course, to have a real confusing mess ... we could have an SE of an SD, 
right?
=============================================================
Richard E. Strauss                      (806) 742-2719
Biological Sciences                     (806) 742-2963 Fax
Texas Tech University                   [EMAIL PROTECTED]
Lubbock, TX  79409-3131
<http://www.biol.ttu.edu/Strauss/Strauss.html>
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