At 6:29 PM -0400 18/9/98, Doggett, David wrote:
>I apologize for the lengthy e-mail. But this is certainly a juicy topic
>for discussion.
Dear David,
Your outline of the background to a Bayesian approach to hypothesis testing,
and how that relates to diagnostic testing was clear and informative.
Two points arise for me:
You wrote:
Also, P(+T I Ha) / P(+T I Ho) is called the likelihood
>ratio (for alpha of 0.05 the likelihood ratio is 95/5=19), which in
>diagnostic testing is the ratio of sensitivity to the false positive
>probability, which is what is plotted on the ROC curve derived from
>signal detection theory.
Firstly: Am I right in thinking this is the likelihood ratio for a postive test
result, and that there is a different formula for LR negative?
Secondly: Your likelihood ratio of 19 seems to be based on a power of 0.95,
and seems to me to be totally dependent on it, thus not necessarily valid for
all p values, as readers of hypothesis test results often do not have power
informaton
to combine with the p value information and should not assume that all p
values of
0.05 give a LR positive of 19.
Ed Loughman
Prince of Wales Hospital
Sydney
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