I am unaware of others' objections to using N-1 as the denominator of sample
variance to eliminate bias in the estimation of population variance, but I
can note one "fly in the ointment." Unbiasedness is defined on the expected
value (mean) of the sampling distribution, not the median, and the
distribution of sample variances has a distinct positive skew (especially
with small df), thus, more often than not, the sample variance is an
underestimate of the population variance, even though it is "unbiased."
This, by the way, makes the distribution of Student's t more leptokurtic
(fat in the tails) than is the normal z, and accounts (along with t's
greater variance) for the critical value of t being larger than that of z,
especially with low df.
John also asked why the loss of 1 df. We loose 1 df because, in our
estimate of the population variance, we had to estimate one other parameter,
the population mean (estimated by the sample mean when computing the sum of
squared deviations about the mean). With the independent samples, pooled
variance, t, we estimate two population means, thus df = N-2.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++ Karl L. Wuensch, Department of Psychology, East Carolina University,
Greenville NC 27858-4353 Voice: 252-328-4102 Fax: 252-328-6283
[EMAIL PROTECTED] http://core.ecu.edu/psyc/wuenschk/klw.htm
