I am going to try to stick to the statistics-related parts, in
replying to Jim Steiger.
With a fake user-name, JS wrote on Thu, 15 Feb 2001 17:34:15 GMT,
[EMAIL PROTECTED] (Irving Scheffe):
JS > "Rich:
"To be blunt, although your comments in this forum are often
valuable, you fell far short of two cents worth this time.
"This is not a popularity contest, it is a statistical argument. "
- I say, if your 'statistical argument' about 'populations' is
rejected by large (and growing) fraction of all statisticians, then I
think you do have to go back to defend your textbook, or show how your
argument differs from what I think it is. That's what I was getting
at by mentioning textbooks.
< snip, verbiage; Jim cited me, RU >
> > - and if you want to know something about how unlikely it was to
> >get means that extreme, you can randomize. Do the test.
JS >
"a. You do *have* means 'that extreme.'
"b. There is no 'likelihood' to be considered, because the entire
population is available. We were assessing the original MIT conjecture
that to imply there were important performance differences between
male and female biologists AT MIT would be 'the last refuge of the
bigot.'"
Given group A and group B, I can do a t-test. Or something.
That will give me a quantification that I did not have before.
Is such a test interesting? - If I am really in a 'population'
circumstance, that question can hardly arise; I would know that
the test tells me nothing. It has nothing to do with taking a vote,
or providing services to a fixed population.
Why does Jim call some means 'extreme'? - in a theoretical
'population', you have means that *exist*. Right now, I think that
it is difficult to justify applying any such adjectives, if you regard
the set of numbers as a 'population.'
I am pointing out: Jim claimed that the productivity of the Men was
impressively greater than that of the women; and that was an act of
inference on his part. So, his act is screwed up, twice: He does a
bad deduction / wrong inference (by ignoring p-level -- in this
instance, apparently ignoring the strong impact of an outlier), and
then he wrongly claims immunity from the standards of inference.
That is, he ought NOT to use means when there are huge outliers that
mess up the t-test; and he ought to find a way to use a p-level for
support.
I have said this a number of times: if you extract meaning, if you
make inferences, then you are treating the population as a sample.
That is what we do in science, and what we do in almost any occasion
where we are publishing for people who are not 'administration.'
And that is why we seldom use the set of statistics for 'finite
populations' and why we do use tests of inference.
JS >
"So, my countercomments to you are:
"1. Rather than snipping the Gork example, deal with it. Explain,
in detail, why the Gork women shouldn't be paid more than the men.
My prediction: you can't, and you won't."
In detail: I think that it is a wretched example.
I still can't figure out what it is supposed to exemplify.
But I can comment on the problem.
===== problem summarized
Productivity,
Females: (91, 92, 93)
Males: (89.5, 90, 90.5)
Why should not Females be paid more, if that's what matters?
======
Based on a t-test, Females might test as having a higher mean.
With a few more cases, that difference would be 'significant' with
either parametric or rank-testing.
But if the natural meaning of production is being used,
then there would be a natural zero, and one should OBSERVE:
all of these scores are confined to a tiny per-cent range.
In fact, the range seems too tiny to be real. Eventually, I
conclude that I don't understand the mechanism of generating the
scores, and/ or someone has been 'cooking the books' or faking
the numbers.
If there were a few more subjects added to each Sex, in
the same narrow range and pattern, I would conclude that there
DEFINITELY was something phony going on.
If pay is to be meritocratic, that would seem to justify a TINY
difference in wages. Nothing about quality. Piece work, I assume.
Sampling of 3 versus 3 is small N; it is far worse than 6 vs 6.
If this is supposed to be about 'statistical power':
In the MIT citation data, the "large difference" between M and F
*would* be significant if there weren't something fishy.
< snip, rest. #2 and #3 - (2) seems to have been answered, and
(3) seems to be a contentious followup to the artificial example that
I scarcely understand in the first place. >
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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