Nico van Duijn is being provocative ... !!
[By the way, I did *not* argue for talking beta=1 (i.e. alpha=0 or no
Type I error): it was given as an extreme case corresponding to ignoring
the data].
Alpha, beta and the differencefor which beta woud be obtained are in
principle pre-trial design factors, which predict the performance of the
trial as designed (in practice you may not have a good notion of them
numerically until you have had the chance to analyse the data, but that
is another story).
However -- and here I find myself, I think, beside Nico -- one meets
cases like the following. There is a limited number of patients available:
say "up to 60" or "up to 200". For any hypothetical difference between
the two treatments, there will be a beta for each alpha. You can turn
this round and calculate the difference X such that the trial, using
critical significance level alpha=0.05 (say) has power beta=0.80 (say).
Trial reports tend to be unacceptable for publication unless they include
a "power calculation". So the protocol includes a section which concludes
"At 5% significance, the trial has 80% power to detect a difference of X"
(but see below).
Honour is now satisfied. You run the trial, do the analysis, and check
whether you get 5% significance or better. If so, you submit it for
publication and, all going well, it will probably be accepted. If not,
then there may be all sorts of reasons why it never gets published; maybe
the article doesn't even get written ...
If you don't have all the information you need to calculate X before the
event, then you can of course estimate X after the event, from the data.
In such cases, the (alpha,beta) have been stripped of predictive relevance
to the trial design (at least partially). Where does this leave us on the
Evidential front?
This is certainly one type of case where the use of Confidence Intervals
evades some difficulties.
Ted.
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E-Mail: (Ted Harding) <[log in to unmask]>
Date: 19-Jan-99 Time: 13:40:17
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