variance and degrees of freedom 
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 variance and degrees of freedom

On those nights that my wife goes to her book club meetings we usually go out
to eat with another couple whose wife also belongs to the book group. We did
so tonight, and I used the opportunity to ask the husband, who teaches
statistics at the School of Business at Stanford, about the use of N versus
N-1 in computing variance. I told him that I gathered it had to do with
degrees of freedom, and he said that that was definitely the case. He also
agreed with the remark in my previous message that N and N-1 corresponded to
population variance and sample variance, respectively. He said that if you
know the population size you can use N safely, but that in *all* the work he
and his students do, they are using samples, and the population size is
unknown, that is, they have lost one degree of freedom. This being the case,
it can be shown that the proper adjustment to make is to use N-1 instead of
N. He said that a similar situation arises in regression analysis, where one
might have lost more than one degree of freedom. I hazarded the guess that in
such cases one would use N-k where k is the number of degrees of freedom
lost, and, yes, he said, that is exactly the case.

We ate at the 3 Fish restaurant on El Camino Real in Menlo Park (just north
of Palo Alto) and the meal was delicious.

Eugene McDonnell



Sat, 14 Sep 2002 03:00:00 GMT  
 
 [ 1 post ] 

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