Raul Miller wrote: > On 6/26/07, John Randall <[EMAIL PROTECTED]> wrote: >> Raul Miller wrote: >> > I am rather dubious of any context where that's a significant >> > issue. >> >> Actually, you have to rely on this: the sample variance with (n-1) in >> the denominator is an unbiased estimator of the population variance: >> with denominator n, it is not. > > I believe I understand the reasoning -- that if you know that you > are computing standard deviation and you have n-1 deviations that > you know also know the nth (subtract the sum of the rest from > zero). > > Or, put more qualitatively, it can be said to be a slight exaggeration > of the deviation to account for the fact that our mean is probably > slightly off. > Raul:
Your explanation is entirely correct. However, the small n problem does arise quite often in practice. A lot of experiments are done with small n because it can be very expensive to increase it. The sample standard deviation appears in all the statistics for comparing means, and you certainly need to take account of it. The significance of the denominator comes in more in multifactor experiments. Although you may have a lot of subjects, they are sliced several ways. The major inferential technique is analysis of variance, where you are comparing ratios of variances on the slices. The denominators can have a significant effect here (and appear as degrees of freedom, for example in the F statistic). Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
