>On 12 Mar 2001, Radford Neal wrote:
>> Yes indeed. And the context in this case is the question of whether
>> or not the difference in performance provides an alternative
>> explanation for why the men were paid more (one supposes, no actual
>> salary data has been released).
>>
>> In this context, all that matters is that there is a difference. As
>> explained in many previous posts by myself and others, it is NOT
>> appropriate in this context to do a significance test, and ignore the
>> difference if you can't reject the null hypothesis of no difference in
>> the populations from which these people were drawn (whatever one might
>> think those populations are).
jim clark <[EMAIL PROTECTED]> wrote:
>Personally, I am not interested in the question of statistical
>testing to dismiss the alternative explanation being proposed;
>indeed, I suspect that the original claim about gender being the
>cause of salary differences would not stand up very well either
>to statistical tests. But there does seem to me to be more than
>just saying ... "see there is a difference" and that statistical
>procedures would have a role to play. For example, wouldn't the
>strength and consistency of the differences influence your
>confidence that this was indeed the underlying factor?
One would want to make some judgement of whether the difference was of
a magnitude that could sensibly be regarded as important. This cannot
be done by a statistical test. In the case at hand, the difference is
so large that no one could sensibly maintain that it is too small to
be a relevant factor in salaries. Of course, there is plenty of room
to debate whether citation counts are actually a good measure of
performance, but the question isn't whether or not MIT's merit scheme
(whatever it is) could be improved, but rather whether it was discriminatory.
>The same
>difference in means due to one or two outliers would surely not
>mean the same thing as a uniform pattern of productivity
>differences, would it?
It wouldn't "mean the same thing" for some purposes, but whether or
not some people are "outliers" is not relevant for deciding whether or
not THESE people might be paid more because they are more productive.
>And wouldn't you want to demonstrate that
>there was a significant and ideally strong within-group
>relationship between productivity and salary before claiming that
>it is a reasonable alternative for the between-group differences?
Yes, one would like to look at the within-group relationship, and this
would come about naturally if one simply computed the standard error
for the gender effect in the normal way - which does NOT involve
testing the significance of the between-group difference in
productivity. It's not possible to do any of this, however, since MIT
hasn't released the data. The whole discussion is about whether the
conclusion in an MIT report, based on unreleased data on salaries,
might be incorrect because of the differences in productivity between
the two groups. Criticism of this conclusion must inevitably be based
only on whatever data is available.
Radford Neal
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Radford M. Neal [EMAIL PROTECTED]
Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
University of Toronto http://www.cs.utoronto.ca/~radford
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