I think the point of the article that if I recall correctly prompted
this discussion was simply that a report of a hypothesis test should
give the actual p-value, not just whether or not it was less than 0.05
(or whatever), the reason being that that way the reader can tell just
how strong the evidence against the null is.
Contrary to some posts, I think situations with believable null
hypotheses do exist. For instance, you might be interested in whether
two genes are or are not on the same chromosome, and have linkage data
to address this question. The quite believable null hypothesis would
be that the genes are on different chromosomes, and therefore are
completely unlinked.
I think the proper role of hypothesis testing is as a rather informal
check of a hypothesis that you suspect may be true (at least to a
degree of approximation that is greater than anything you could hope
to measure). The choice of test statistic is a rough way of
expressing what the likely sort of alternative is, without formally
specifying it. If you get a small p-value, you may suspect something
is wrong with the null hypothesis.
Viewed this way, the whole procedure is of the rough-and-ready sort,
suitable only for situations where you don't have the time to
formulate a proper Bayesian model. It's by attempting to make more of
it than this that people get into trouble. For instance, they may
start to think, as some posters here seem to, that the p-value is the
probability that the null hypothesis is true, which it isn't.
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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