In article <[EMAIL PROTECTED]>,
Will Hopkins <[EMAIL PROTECTED]> wrote:
>I've been involved in off-list discussion with Duncan Murdoch. At one
>stage there I was about to retire in disgrace. But sighs of relief... his
>objection is Bayesian. OK. The p value is a device to put in a
>publication to communicate something about precision of an estimate of an
>effect, under the assumption of no prior knowledge of the magnitude of the
>true value of the effect.
The p value does not communicate anything about the precision
of anything by itself.
If we assume no prior knowledge of the true
>value, then my claim stands: the p value for a one-tailed test is the
>probability of an opposite true effect--any true effect opposite in sign or
>impact to that observed.
This is likewise false. For a translation parameter, with a
uniform prior, it is correct, but only in this too often
assumed, but also unreasonable, situation. The use of this
prior as meaning "no prior knowledge" may lead to reasonable
actions, but for deciding whether the new or the old is better,
the p-value to use becomes 0.50.
>I can't see how a Bayesian perspective dilutes or invalidates this
>interpretation. The same Bayesian perspective would make you re-evaluate
>the p value under its conventional interpretation.
There is no way to use the present p-value by itself correctly
with additional data.
In other words, if you
>have some other reason for believing that the true value has the same sign
>as the observed value, reduce the p value in your mind. Or if you believe
>it has opposite sign, increase it.
With composite hypotheses, one cannot simply use Bayes factors.
>If we are stuck with p values, then I believe we should start showing
>one-tailed p values, along with 95% confidence limits for the
>effect.
The only reason p values are used as they are is that they have
become religion.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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