Dear Jim:
1. Regarding my email signature, it is a spam-virus deflector.
Sorry you were confused. I've had 3 virus attempts already this week.
I'm really Jim Steiger -- see signature. I'm not really Irving
Scheffe.
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. 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.
Maybe the following example will help make
it clearer:
----- Example: Blurk Productivity in the Kingdom of the Gorks -----
There are 6 living Gorks, 3 of them female. A feminist
Gork asserts that currently living female Gorks are underpaid,
because they are earning the same money as currently living male
Gorks, but they produce more blurks than male Gorks, and blurks are
the sole index of personal worth in Gork society.
The following hidden blurk production figures suddenly become
available. [Assume these figures are, for each Gork, permanent
and unchanging.]
Females Males
------- -----
91 89.5
92 90
93 90.5
The head Female asserts that these data prove her assertion.
"We always produce more blurks. We are better Gorks. We
should be paid more," she says.
But the male Gorks have something up their sleeve. They hire
Gene Gallagher, who says, "No, a statistical randomization test the
.01 level fails to find a significant difference between Female and
Male Gorks. Consequently we do not have enough evidence to change the
salary structure."
----------------
Who is right?
Answer.
There is no question who is right. The feminist Gork leader is
correct. Start paying the Female Gorks what they are worth!!
Distributional questions are irrelvant.
Questions of power are irrelvant.
All the machinery of hypothesis testing [be it
parametric or nonparametric] is irrelevant.
A statistical hypothesis test is not only unnecessary but
inappropriate, be it a t-test or a randomization test.
You are not interested in testing the hypothesis that Female Gorks are
better blurk producers than Male Gorks in some hypothetical
population.
You are even less interested in fanciful combinatorial questions about
what would happen if you randomly shuffled the
6 scores. Why would one want to mumble aimlessly about
what would happen if you shuffled the two stacks of numbers?
First of all, no random shuffling was involved,
so the probability model is not correct for the data at hand,
although the calculation about fanciful shuffling is correct,
and trivial. One can, of course, compute a combinatorial probability
(.05) from this information. But such a probability, though
interesting, and "correct," is, like the T test, completely irrelevant
to the question at hand, and inappropriate as a probability
model for the data.
You are *ascertaining* whether the living Female Gorks are better
blurk producers than the living Male Gorks. And, as anyone can see
[who wants to], they are.
Start paying the 3 females what they are worth!! It is a simple,
undeniable fact that they are better blurk producers.
---------------
All the best,
Jim Steiger
James H. Steiger, Professor
Department of Psychology
University of British Columbia
Vancouver, B.C., Canada V6T 1Z4
On Wed, 14 Feb 2001 21:04:29 -0600, jim clark <[EMAIL PROTECTED]>
wrote:
>Hi
>
>I'm not too sure who presented the following example, as the
>e-mail account and the signature (see below) were
>different. Nor was I completely clear what point was
>being made with the following analogy. Anyway, ...
>
>On Wed, 14 Feb 2001, Irving Scheffe wrote:
>
>> let me suggest the following potential exam question for you,
>> and your students.
>
>> 4. (10 points). [Disclaimer: this is a hypothetical example.]
>
>> The white players on the Detroit Pistons believe that they
>> are victims of salary discrimination. They have discovered
>> that the black players have higher salaries.
>...
>
>> The NAACP felt that this analysis was biased, and incomplete.
>> It gathered performance data on the players on the Pistons.
>> Figures are points per 48 minutes of playing time. [This
>>
>> White Black
>> -------------
>> 12.8 13.7
>> 11.1 22.3
>> 19.9 20.9
>> 13.9
>> 16.8
>> 17.1
>> 13.0
>> -------------
>>
>
>> Salary data are not available, as the club has declared them
>> confidential. The NAACP points out that, however, the black
>> players have higher performance than the white players. The
>> mean performance for the black players is 16.83, for the
>> white players 14.6. According to the NAACP spokesman,
>...
>
>> At this point, a spokesman for the white players, Gene
>> Gallagher, intervenes. Gene considers himself an expert
>> statistician. Gene says that, "No, actually these data don't
>> show that the black Pistons players have been producing more
>> than the white players. I performed a t-test, and found
>> t=.82, df=8, non-significant. The Pistons' black players have
>> not performed significantly better than the Pistons white
>> players." The NAACP spokesperson responds. "No Gene. The
>> question is not whether the data from the Pistons allow us to
>> generalize about all white players vs. all black players.
>> IF the Pistons data represented random sampling, and IF we
>> were interested in answering questions about ALL black and
>> white players, THEN your analysis might be relevant."
>
>> "But we weren't trying to answer that question, and we do not
>> believe that the Pistons represent a random sample. We were
>> simply interested in whether the Piston black players had
>> performed as well as the Piston white players. Statistical
>> testing is inappropriate, and, in fact, misleading."
>
>> Who is right? Gene or the NAACP? Why?
>
>> --------------------------
>> James H. Steiger, Professor
>> Department of Psychology
>> University of British Columbia
>> Vancouver, B.C., Canada V6T 1Z4
>
>I might be wrong, but the implication seems to be that the
>statistical test was inappropriate. However, isn't it the case
>that the standard statistical inferences are also consistent with
>(i.e., supported by) randomization procedures? In the present
>case, the t-test means that if one randomly chose 3 of the 10
>scores to be identified as white, then there is a high
>probability of obtaining a difference as large as that observed
>in the actual data. So statistical tests are appropriate even
>when one is _not_ generalizing to a population.
>
>Best wishes
>Jim
>
>============================================================================
>James M. Clark (204) 786-9757
>Department of Psychology (204) 774-4134 Fax
>University of Winnipeg 4L05D
>Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
>CANADA http://www.uwinnipeg.ca/~clark
>============================================================================
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