Stan Brown wrote:
I see why the quality controller would want to
> do a two-tailed test: the product should not be outside
> manufacturing parameters in either direction. (Presumably the QC
> person would be testing the pills themselves, not patients taking
> the pills.)
Actually, the quality controller's test is a slight misnomer here,
because we aren't talking in this problem (as you more or less observed)
about standard QC methodology. Standard QC doctrine, from what I hear,
generally goes for repeatability, and "better than specified" is *not*
good. ("So, how did you do in the QC Methods exam?" "My score was three
sigmas above the class average... so the prof failed me.")
The question dealt with a situation, though, in which only one
direction of deviation is bad. Thus, the test might legitimately be
one-sided. The reason is that the alpha value represents the risk of
unnecessarily stopping the production line, reprinting the labels, or
whatever. You *don't* need to do this if the product works better than
advertised, so a one-sided alpha really is the risk of doing it
unnecessarily.
> But I don't see why either the advertiser or the consumer advocate
> would, or should, do a two-tailed test.
The idea is that the "product" of these tests is a p-value to be used
in support of an argument. The evidence for the proposal is not made any
stronger by the tester's wish for a certain outcome; so the tester
should not artificially halve the reported p-value.
Superficially, the idea of halving your p-values, doubling your chance
of reporting a "statistically significant" result in your favored
direction if there is really nothing there, and as a bonus, doing a
David-and-Uriah job ("And he wrote in the letter, saying, Set ye Uriah
in the forefront of the hottest battle, and retire ye from him, that he
may be smitten, and die.") on any possible finding in the other
direction, may seem attractive. A moment's thought should persuade us
that it is not ethical.
-Robert Dawson
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