Michael Quanty asks:
>
>Why is 1 the magic number? I see how it makes more radical corrections for
>smaller sample sizes. But was it chosen for a theoretical or practical
>considerations.
>
The intuitive explanation is that the variance is computed on the
deviations of scores around the mean, which itself must be computed. Once
we know what the mean is, only N-1 scores are free to vary randomly (the
last one must make the sum equal N * Mean). But this doesn't really tell
us why the variance computed with N-1 is an unbiased estimate of the
population variance. There is a relatively short proof that the expected
value of the variance computed with N-1 equals the population parameter. I
will have to play a Stephen Black here: my notes with this proof are
buried in some ancient file of stat notes from grad school days (if I still
have them).
Perhaps a colleague on TIPS who has this proof closer to hand can help me out.
I will also confirm John Kulig's comment that while the variance (computed
using N-1) is an unbiased estimator of the population variance, the square
root of the variance (SD computed using N-1) is _not_ and unbiased
estimator of the population SD. I've forgotten the mathematical
particulars for why that happens. As somebody probably said: "The proof
is out there." (Sorry, couldn't resist.)
Claudia
________________________________________________________
Claudia J. Stanny, Ph.D. e-mail: [EMAIL PROTECTED]
Department of Psychology Phone: (850) 474 - 3163
University of West Florida FAX: (850) 857 - 6060
Pensacola, FL 32514 - 5751
Web: http://www.uwf.edu/psych/stanny.html
