🚀 go-pugleaf

In article <1992Aug14.231916.23479@magnus.acs.ohio-state.edu>, regeorge@magnus.acs.ohio-state.edu (Robert E George) writes:
>
>
.>> (LOTS OF INTERESTING STAFF DELETED TO PRESERVE SPACE)

>I'm not certain what "underestimate" means here: if you are speaking of
>bias (bias being the difference between the estimand and the expected
>value of the estimator), then
>
>        ---  _        _
>        \   | X - Xbar |2
>T =     /   |_        _|
>        ---
>       ------------------
>               n
>
>will "underestimate" the population variance *for any sample size n*.
>T will always have a negative bias *regardless of how large a sample is
>used to compute T*.
>
>More intuitively, if we take a very sample, we are less likely to get
>extreme values and so our notion of what the population variance is (note
>that I am not proposing some particular estimator) will be unrealistic.
>For instance, I give an exam to two students. Their scores are 67 and
>71. I think, "Gee, there's not a lot of variability in these scores."
>But then 8 more students take the exam:
>     60 78  100 38  50 88  99 39
>
>and it now is clear there *is* more variability in these scores.
>
>But let me reiterate that T will *always* have a negative bias for the
>population variance whatever the sample size is

MY IGNORAMUS QUESTION? Does't that negative bias decrease as the sample
size approaches population size? 

thanks in anticipation for answering my question.
Mokaba