Re: Is this sample representative of the population?


Z wrote:

in response to

> "David Winsemius" <dwin$emiu$@comcast.net>

whose first response had many sensical points.
>
> "Richard Ulrich" <Rich.Ulrich@xxxxxxxxxxx>

whose response was nonsensical and off the wall, as usual.


> Any further thoughts? I'd be grateful.
>
> Z

I was attracted by the question in your SUBJECT, because that's
the first issue I discussed with my undergrad students taking their
first course in statistics about the idea of a "random sample" and
whether such a sample is "representative" of the population.

In that respect, all of you (except part of what Winsemius wrote)
missed the boat! This line of Winsemius captures the appropariate
answer to your question:

DW> Whether the results of a survey are representative may lie
DW> not in the data but in the sampling method.

except he didn't give the elaboration which I'll provide below.


A "SIMPLE random sample" is NOT supposed to be representative
of ANY population. It merely assures that each sample of the same
size has the same chance of being selected. In other words, a
simple random sample merely assures an "equal opportunity of
selection of every possible sample of the given size".

This is actually one of the DEEP philosophical issues in the use
of "randomization" in classical statistical design of experiments!
There ain't no such thing as a truly random sample in practice,
because the sampling statistician would DISCARD many of the
valid (simple random) ones because they look too nonrandom.


Thus, if a SIMPLE random sample of size 10,000 is selected from
the US population of 200,000,000 say, then what it means is that
each of the combinations of C(200,000,000; 10,000) of the subsets
of the population has the same probability 1/C(200,000,000; 10,000)
of being selected!

So, the probability of having selected a sample of the 10,000
<tallest, shortest, dumnest, smartest, ...> of the population is the
SAME as the probability of selection of any other "simple random
sample" of size 10,000.

That's WHY, for most polls, a STRATIFIED sampling method is
used, to ENSURE that the most important characteristics of the
selected sample are "representative" of the population in THOSE
stratified characteristics. for the PURPOSE of the study based
on a poll. I took the first of 912,000 web pages Google found
when I specified the keywords "stratification in sampling":

http://www.mis.coventry.ac.uk/~nhunt/meths/strati.html

It's a very elementary example illustrating the notion of
stratification in sampling.


Any characteristic that is SUBSTANTIVELY important to be
represented in a poll must be pre-selected before simple random
samples are selected WITHIN those strata.

For example, if a poll is about a political issue in the USA, then
it is imperative that the sample be stratified according to the
proportions of Democrats and Republicants, for the sample
to be representative of the POLITICAL views of the population.

Otherwise, a SIMPLE random sample, or a telephone poll,
or some other method of random selection WITHOUT
stratification may produce a sample of 10,000 consisting
entirely of Republicants who are Southern Baptists, or
10,000 consisting entirely of Catholics. Extremely unlikely,
but just as likely as any OTHER combination under the
simple random sampling scheme.


For MARKETING research, there are different reasons for
different stratifications. Some of the common strata are
Age, Economic status, gender, etc.

Thus, the proper answer to your question is NOT what
statistical test to apply on the data (any such test will be
a MISapplication of statistics to the question asked).

Perhaps that is the reason the client asked whether the
samples are "representative", to see if the consultant is
aware of the issue of stratification for the INTENDED
purpose of a sample poll/collection; or whether the
consultant is blinding pulling some t-test, chi-square-
test, contingency tables out of their padantic posterior
which would always address the WRONG questions
from the one asked, if those tests are even applicable
to the data collected.

-- Reef Fish Bob.

P.S. I am listed as by my posting address instead of my
posting name of "Reef Fish" because I am NOT a
Google subscriber to the sci.stat.consult group.

This is the first post I've ever made that is posted solely
to this group.

.

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