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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