In article <p0433010fb6d329af7d2d@[139.80.121.126]>,
Will Hopkins <[EMAIL PROTECTED]> wrote:
>At 7:34 PM +0000 12/3/01, Jerry Dallal wrote:
>>Don't do one-tailed tests.
>If you are going to do any tests, it makes more sense to one-tailed
>tests. The resulting p value actually means something that folks can
>understand: it's the probability the true value of the effect is
>opposite to what you have observed.
>Example: you observe an effect of +5.3 units, one-tailed p = 0.04.
>Therefore there is a probability of 0.04 that the true value is less
>than zero.
This is certainly not the case, except under highly dubious
Bayesian assumptions.
>There was a discussion of this notion a month or so ago. A Bayesian
>on this list made the point that the one-tailed p has this meaning
>only if you have absolutely no prior knowledge of the true value.
>Sure, no problem.
This is not possible; the idea of "insufficient reason" is
full of contradictions, and is a major reason for the failure
of Bayesian inference to be pursued in the 19th century.
There is generally a prior probability that the effect will
be small. Unless there are enough observations that the
scale of "small" is so spread out that it looks large, the
probability statement you have made does not have any real
justification. Also, should you care if the difference is
that small?
>But why test at all? Just show the 95% confidence limits for your
>effects, and interpret them: "The effect could be as big as <upper
>confidence limit>, which would mean.... Or it could be <lower
>confidence limit>, which would represent...
Fixed coverage confidence limits, either classical or
Bayesian, likewise are not appropriate from the real
problem, which is what action to take.
Therefore... " Doing it
>in this way automatically addresses the question of the power of your
>study, which reviewers are starting to ask about. If your study turns
>out to be underpowered, you can really impress the reviewers by
>estimating the sample size you would (probably) need to get a
>clear-cut effect. I can explain, if anyone is listening...
This is more than one can do. Consider ALL the consequences
of the action; you only look at some of them. Also, do this
in ALL the states of nature.
--
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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