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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