In article <008201c14763$9392f260$e10e6a81@PEDUCT225>,
Paul R. Swank <[EMAIL PROTECTED]> wrote:
>I use to find that students respoded well to the idea that the hypothesis
>test told you, within the limits of likelihood set, where the parameter
>wasn't while confidence intervals told you where the parameter was.
>Paul R. Swank, Ph.D.
>Professor
>Developmental Pediatrics
>UT Houston Health Science Center
Neither of these is correct. A hypothesis test tells you
nothing of the sort, and neither does a confidence interval.
A 95% confidence interval tells you that a process has been
used which has the property that, BEFORE the data were
analyzed, 95% of the time the parameter would be in the
computed interval. A test of hypothesis at the .01 level
tells you that the probability that a sample that extreme
would arise by chance IF THE NULL HYPOTHESIS IS EXACTLY
TRUE is less than .01. Neither statement corresponds to
a probability statement AFTER the observations have been
analyzed.
To get a probability statement after the observations have
been analyzed, one needs a prior, from which posteriors can
be calculated using Bayes' Theorem. This is not the only
possible basis for action, but I can there are no procedure
which stand the test of self-consistency for classical
significance tests, and while there are some for confidence
intervals, they correspond to quite unreasonable evaluations
of the consequences of the choice of an interval.
--
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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