
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 misstatement 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.)?

