Irving Scheffe wrote:
> Imagine it is 1961. Our question is, which outfield has better
> home run hitters, the Yankees or Detroit? Here are the numbers
> for the Yankee and Tiger starting Outfields.
>
> Yanks Tigers
> ----- ------
> 61 45
> 54 19
> 22 17
> --------------
>
> Now, the t-test isn't significant, nor is the permutation test.
> But is either relevant to the question? If you have a reasonable
> understanding of the notion of "home run," the answer is no.
>
<snip>
> It was, by definition, the population of interest, so it appears that
> you are flat wrong. The question we were asking was, "if we take the
> large identifiable cluster of senior MIT women who graduated between
> 1970 and 1976, and compare them with their natural cohort, the men who
> graduated in the same time frame, do we see performance differences?"
>
> The answer is, as shown by the data above: yes. We see huge
> performance differences. Just like with the Yankees and Tigers in
> 1961.
It seems to me that you are unncessarily restricting the questions than can be
asked by others. You are not even restricting them to the interesting
questions. For example, asking who scored more in 1961 - is different to which
players were better. Why not think of it in terms of "Could this difference be
produced by 6 players of equal ability influenced by a large number of random
factors". In that case a significance test might have some value in evaluating
the hypothesis that one group was better.
The second case is even stronger. Take any two groups any you'll almost
certainly find a difference on most measures (citation count, salary, hat size
or whatever).
Finally, what allows you to infer that any difference you observe it "huge".
This is a relative judgement. In statistics we typically reference it to some
indication of (population) variability. In real world contexts we often use
other benchmarks.
For example, think about runs scored in the first innings of a test match by
three top order batsmen from two cricket teams
England Sri Lanka
----- ------
61 45
54 19
22 17
--------------
Is this a huge difference? I think not. Does it provide strong evidence that
the England top order batsmen are better than the Sri Lankans? No. What allows
you to infer a huge difference in the baseball case is your knowledge of
baseball (frequency of runs and so on). So at best, I think it is a misleading example.
Thom
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