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Topic: Sampling From Finite Population with Replacement
Replies: 28   Last Post: Sep 30, 2010 6:30 AM

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 cagdas.ozgenc@gmail.com Posts: 58 Registered: 3/29/06
Re: Sampling From Finite Population with Replacement
Posted: Sep 29, 2010 3:39 PM

On 29 Eylül, 23:09, Rich Ulrich <rich.ulr...@comcast.net> wrote:
> On Tue, 28 Sep 2010 21:21:42 -0700 (PDT), Cagdas Ozgenc
>
> <cagdas.ozg...@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

I am glad that we are now at least on the same ground.

If I look at the definition of Sampling Bias in Wikipedia it is
actually exactly what you describe above.

http://en.wikipedia.org/wiki/Sampling_bias

Even though I understand you, I don't understand why you think I am
wrong. Is it the definition of the word "bias" that we differ in
opinion? If so according to which source (book, article, etc.)?