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Re: Sampling From Finite Population with Replacement
Posted:
Sep 29, 2010 3:09 PM
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On Tue, 28 Sep 2010 21:21:42 -0700 (PDT), Cagdas Ozgenc
<cagdas.ozgenc@gmail.com> wrote:
>
>> I agree that the above is ambiguous if you really want to press
>> the point. It uses mu and sigma which describe populations
>> It does not state whether the population is the class of 2005,
>> or something wider that would be more useful for generalization.
>>
>
>That's not the issue. Take any finite population with a data
>generating process behind it. Population mean is an unbiased estimate
>of data generating process distribution as Ray pointed out. But once
>you start getting samples from that population your random error turns
>into a systematic error (a bias).
That's clever, but basically wrong. That is not the definition
of bias that we have in play previously.
You can get closer and closer to obtaining the value of
the population mean; but you never have more precision
than what the population mean provides, in regards to
estimating the underlying process.
So? That is the error of a single sampling (the "population").
Yes, colloquially speaking, we say that any single drawing of
a sample is going to be biased, or it gives a biased estimate.
But the relevant meaning when we speak of "an unbiased
statistic" is limited to the venue of the procedure that is being
repeated.
Subsamples give an unbiased estimate of the sample.
The sample gives an unbiased estimate of the generating
process -- and the mean of the whole sample has smaller error
than any of its subsamples will have. Technically, we want to
say that subsamples *do* give an unbiased estimate of the
generating process, (inevitably) with larger error than the
whole sample.
The prospect of mis-statement arises from imagining that
using the subsamples can escape the original error of the
sample. Even though we may casually call it "biased" when
we describe its effect, that is applying the adjective on a
different level of intercourse.
--
Rich Ulrich
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