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.
Michael S: Don't even think about referring me to Three Dog Night.
Michael B. Quanty, Ph.D.
Psychology Professor
Senior Institutional Researcher
Thomas Nelson Community College
PO Box 9407
Hampton, VA 23670
Phone: 757.825.3500
Fax: 757.825.3807
-----Original Message-----
From: Claudia Stanny [mailto:[EMAIL PROTECTED]]
Sent: Monday, September 25, 2000 10:46 AM
To: [EMAIL PROTECTED]
Subject: N versus N-1 [Was: Another Standard Deviation question]
>From: "James D. Dougan" <[EMAIL PROTECTED]>
>Subject: Another Standard Deviation question
>
>Back in the "good old days" all (or at least most) of the undergraduate
>statistics texts taught the standard deviation using ther "N-1" formula.
>The "N" formula was perhaps mentioned in a footnote, but often not
>mentioned at all...
>
>Now, virtually all of the texts teach the "N" formula in the beginning
>under descriptive stats, then introduce N-1 later under inferential.
>
The formula for computing the sample variance using N as the divisor is the
correct descriptive statistic to compute for the sample variance. As a
descriptive statistic, the variance formula with N as the divisor is
accurate. It is exactly equal to the variance of the sample (whereas the
formula using N-1 is a smaller value). But this statistic is biased as an
inferential statistic (biased in the statistical sense -- the long run
average or expected value of the statistic does not equal the value of the
population parameter it is used to estimate). The variance computed using
N-1 is an unbiased estimator of the population parameter.
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
