Jim,
Unfortunately, the issues are too complex to distilled this way.
If you're arguing in your example, that workers should be paid for
piecework, then fine. So be it. Pay the Detroit Pistons by the
point.
I've got no problem with that.
Often in these cases, performance is not so easily quantifiable.
We often have a group of individuals who are judged comparable in
responsibilities and performance. In such cases, it *may* be
appropriate to use permutation methods. The rationale would be:
There is some variation in salary due to situation-specific
"whatever", so we don't expect everyone to be making exactly the
same
money. One way to attempt to detect discrimination against
a particular group is to ask whether their salaries are consistent
with what one would expect assigning salaries at random without
regard to group membership.
For any particular situation, we can and should discuss whether
the statistical model is a fair representation of what we mean
by non/discrimination, but I think it is as much a mistake to
dismiss it outright without a full discussion as it is to embrace
it blindly.
--Jerry
Irving Scheffe wrote:
> 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.
> ---------------
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