Date: Sep 29, 2010 3:39 PM Author: cagdas.ozgenc@gmail.com Subject: Re: Sampling From Finite Population with Replacement 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.)?