Jim has consistently maintained three claims/arguments:
1. we are not trying to generalize from a small group of people to a larger
population.
2. No inference is involved (if we are not generalizing)
3. Using statsitical tests is meaningless (since no inference is involved).
I agree with his 1st and 3rd points -- but not his 2nd.
Within the second, I disagree with the truth of his premise.
The generaliation mentioned in #1 is NOT the only possible generalization.
Another generalization may be involved: that involving time. We sample
things (basketball goals) for two groups of players in a few games and then
want to make an inference about whether these particular scores were
unlikely given that THESE particular players involved had the same average
scores in the long run -- for all games.
Given a time-based generalization, we now have an inference. Given this
inference, the applicability of statistical tests seems quite relevant.
Milo
PS. This may be a quasi-Bayesian reinterpretation of these problems -- but
if it fits.....
-------------------------------------------------
"Irving Scheffe" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> There are a wide variety of probabilities that may be calculated
> in this situation, depending on the assumptions you want to
> make, and precisely what you mean by "this result." However, if you
> ask, "How likely is it that the for side won", the answer is that the
> for side won. If you ask, "How likely is it that the percentage of
> for votes is higher for women than for men in this sample," the answer
> is that it is perfectly likely, because it happened.
>
> In an example perhaps more relevant to previous examples here, suppose
> this was an actual departmental vote, and the result was 5-3. The
> motion passed.
>
> If one of the men was a statistician wanting to overthrow
> the result and said, "wait a minute,
> let's perform a statistical test and see the probability of
> obtaining this gender split, given that the 5 yes votes were actually
> randomly assigned with respect to gender," I suspect people
> would think him odd. He can compute this probability, but
> it is irrelevant.
>
>
>
>
> On 15 Feb 2001 13:49:51 -0800, [EMAIL PROTECTED] (Paul R
> Swank) wrote:
>
> >I remember a question from some stat book about a situation where there
were 8 members of a group, three men and five women (or the reverse, I can't
remember
> >
> >which) and on some issue the vote was five to three with all five women
voting for. The question was "How likely was this event to occur by chance"?
Can we not ask that question?
> >
> >
> >At 05:34 PM 2/15/01 GMT, you wrote:
> >
> >>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. You offered an unsupported
> >
> >>opinion with only one content-related
> >
> >>comment. Let's cut to the chase.
> >
> >>
> >
> >>Please define precisely what you meant in
> >
> >>the phrase
> >
> >>
> >
> >>> - and if you want to know something about how unlikely it was to
> >
> >>>get means that extreme, you can randomize. Do the test.
> >
> >>
> >
> >>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."
> >
> >>
> >
> >>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.
> >
> >>
> >
> >>2. You talk about "how unlikely it was." Unlikely when?
> >
> >>Unlikely under what conditions?
> >
> >>
> >
> >>3. (if you choose to answer question 2) Why would the Gork society be
> >
> >>interested in assessing any such likelihood, if they have a
> >
> >>meritocracy, and their only interest lies in assessing whether male
> >
> >>and female Gorks have shown productivity differences?
> >
> >>
> >
> >>If you can actually answer such questions, rather than rendering
> >
> >>an unsupported opinion, you might have two cents worth to add.
> >
> >>
> >
> >>All the best,
> >
> >>
> >
> >>Jim
> >
> >>
> >
> >>---------
> >
> >>James H. Steiger, Professor
> >
> >>Dept. of Psychology
> >
> >>University of British Columbia
> >
> >>Vancouver, B.C., Canada V6T 1Z4
> >
> >>
> >
> >>Comments reflect my opinion only,
> >
> >>-------------
> >
> >>
> >
> >>On Thu, 15 Feb 2001 10:39:45 -0500, Rich Ulrich <<[EMAIL PROTECTED]>
> >
> >>wrote:
> >
> >>
> >
> >>>I am just tossing in my two cents worth ...
> >
> >>>
> >
> >>>On Thu, 15 Feb 2001 07:53:13 GMT, Jim Steiger, posting as
> >
> >>>[EMAIL PROTECTED] (Irving Scheffe) wrote:
> >
> >>>
> >
> >>><< snip, name comment >
> >
> >>>
> >
> >>>> 2. I tried to make the Detroit Pistons example as obvious as I could.
> >
> >>>> The point is, if you want to know whether one population performed
> >
> >>>> better than another, and you have the performance information, [under
> >
> >>>> the simplying assumption, stated in the example and obviously not
> >
> >>>> literally true in basketball, that you have an acceptable
> >
> >>>> unidimensional index of performance], you don't do a statistical
test,
> >
> >>>> you simply compare the groups.
> >
> >>>
> >
> >>>
> >
> >>>>
> >
> >>>> Your question about the randomization test seems
> >
> >>>> to reflect a rather common confusion, probably
> >
> >>>> deriving from some overly enthusiastic comments
> >
> >>>> about randomization tests in some
> >
> >>>> elementary book.
> >
> >>>
> >
> >>> - If you are willing, perhaps we could discuss the textbook
> >
> >>>examples. I don't remember seeing what I would call
> >
> >>>"overly enthusiastic comments about randomization."
> >
> >>>When I looked a few years ago, I did see one book with an
> >
> >>>opposite fault, exemplified in a problem about planets.
> >
> >>>I thought the authors' were pedantic or silly, when they refused
> >
> >>>to admit randomization as a first step of assessing whether there
> >
> >>>*might* be something interesting going on.
> >
> >>>
> >
> >>>> Some people seem to
> >
> >>>> emerge with vague notions that two-sample randomization tests make
> >
> >>>> statistical testing appropriate in any situation in which you have
> >
> >>>> two stacks of numbers. That obviously isn't true.
> >
> >>>> Your final question asks if "statistical tests" be appropriate
> >
> >>>> even when not sampling from a population. In some sense, sure. But
not
> >
> >>>> in this case.
> >
> >>>
> >
> >>>I can't say that I have absorbed everything that has been argued.
> >
> >>>But as of now, I think Gene has the better of it. To me, it is not
> >
> >>>very appropriate to be highly impressed at the mean-differences,
> >
> >>>when TESTS that are attempted can't show anything. The samples
> >
> >>>are small-ish, but the means must be wrecked a bit by outliers.
> >
> >>>
> >
> >>>>
> >
> >>>> Maybe the following example will help make
> >
> >>>> it clearer:
> >
> >>> << snip rest, including example that brings in "power" but not
> >
> >>>convincingly. >
> >
> >>
> >
> >>
> >
> >>
> >
> >>=================================================================
> >
> >>Instructions for joining and leaving this list and remarks about
> >
> >>the problem of INAPPROPRIATE MESSAGES are available at
> >
> >> http://jse.stat.ncsu.edu/
> >
> >>=================================================================
> >
> >>
> >
> >------------------------------------
> >
> >Paul R. Swank, PhD.
> >
> ><smaller>Professor & Advanced Quantitative Methodologist
> >
> ></smaller>UT-Houston School of Nursing
> >
> >Center for Nursing Research
> >
> >Phone (713)500-2031
> >
> >Fax (713) 500-2033
> >
> >
> >=================================================================
> >Instructions for joining and leaving this list and remarks about
> >the problem of INAPPROPRIATE MESSAGES are available at
> > http://jse.stat.ncsu.edu/
> >=================================================================
>
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