Spot on, Robert.
Alan
Robert Dawson wrote:
> Joe Ward wrote:
>
> Yes, there occasionally were discussions in our Air Force research
> whether or not we were working with the POPULATION or a SAMPLE.
>
> As Dennis comments:
> |
> | > the flaw here is that ... she has population data i presume ... or about
> | as
> | > close as one can come to it ... within the institution ... via the
> budget
> | > or comptroller's office ... THE salary data are known ... so, whatever
> | > differences are found ... DEMS are it!
> | >
>
> One of my Professors used to use the Invertebrate Paleontologists as his
> example of a POPULATION. I think at that time there were less than 20
> people who were Invertebrate Paleontologists.
>
> OK. Now, suppose that you knew them all, and noticed that ten of them
> drove convertibles. You would probably make some generalization about
> invertebrate paleontologists, consider that this was a genuine phenomenon,
> and assume that if one more invertebrate paleontologist *did* turn up, it
> might well be in a convertible. [Maybe convertibles are easier than sedans
> to get into if you're invertebrate? <grin>]
>
> Suppose there were also exactly two extraterrestrial paleontologists in
> the world, and one of them drove a convertible. You would be less likely to
> think in the same way.
>
> Now, if you discovered that around 50% of the vertebrate paleontologists
> in the world drove convertibles, you would consider that you had ironclad
> proof that something was going on.
>
> I suggest that even if these groups are not true random samples (and
> they are not - more on that later) that the informal inferential process
> described has much in common with formal statistical inference. And, if it
> walks like a duck and quacks like a duck, it makes some sense to cook it
> like a duck. (Similarly, if you were to toss a coin and cover it unseen, and
> offer a frequentist various odds that it had landed heads, most frequentists
> would put their cutoff betweeen accepting and rejecting the wager at odds
> corresponding to a 50% probability, even if they refused to admit that that
> was the probability that the coin was heads-up.) There are obvious problems
> with the sampling technique - though probably less than if a convenience
> sample of (say) the most accessible half the population had been taken.
>
> As far as random samples are concerned: it is *very* rare for a true
> random sample, based on an equal-probability sample of the population to
> which the inference is intended to extend, to be taken. Say a researcher is
> studying the behaviour of humans. (S)he may take a random sample from the
> student subject pool, but not from the human race; and yet the paper
> published will claim to be about "Artificially Inducing The Gag Reflex in
> Humans", not "Artificially Inducing The Gag Reflex in Students Enrolled in
> Psych 1000 at Miskatonic U. (Fall '00)". Even if some future world
> government were to allow researchers access to a list of all humans alive at
> some moment to use as a sampling frame, most researchers would not disclaim
> any applicability of their research to those dead or not yet born. The
> implicit "Platonic" population larger than that available for study is a
> problem that is always with us; a bad sample is one in which this causes
> bias. The situation in which the entire actual population is available for
> study is an extreme case, of course.
>
> -Robert Dawson
>
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--
Alan McLean ([EMAIL PROTECTED])
Department of Econometrics and Business Statistics
Monash University, Caulfield Campus, Melbourne
Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
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