In article <[EMAIL PROTECTED]>,
dennis roberts <[EMAIL PROTECTED]> wrote:
>At 02:11 PM 8/20/00 -0500, Herman Rubin wrote:
>> It is necessary to simultaneously consider all
>> consequences of the proposed action in all
>> states of nature.
>every now and then, herman tosses in this dart ... but, i have never once
>heard him say what the heck this means ... but, i would suspect that it
>IMPOSSIBLE to do ... no mortal can catch up with the 3 things implied by
>his dart ... these are:
>1. it's difficult to do many things simultaneously
>2. we can't possibly know what all the potential consequences are for ANY
>given action
>3. and ... what are "all states" of nature?
I agree that no mortal can do any of these precisely.
Neither can anyone apply Newtonian gravity precisely,
let alone Einsteinian, or carry out even worse physical
calculations. So one must approximate. NASA seems to
have no problem in calculating, when the information at
hand is reasonably good.
The subject of statistics is how to make decisions in the
face of uncertainty, not how some people make decisions.
It is how to do it well, or at least reasonably well. As
this is a difficult problem, we need to use some basic
principles, and the principle of self-consistent behavior
is such. Setting up arbitrary procedures because of
tradition or convenience is not.
One normally ignores the complexities of the full state of
nature, and one normally considers only those consequences
which make much of a difference. But the simultaneous
consideration of these is quite important; the "level" of
one consequence which is to be tolerated depends on the
balance of this against other consequences.
For testing hypotheses, one has to consider not just the
type 1 error, but the type 2 error as well, and its
consequences can depend on the magnitude of the difference
of the parameters. It is necessary to consider them
simultaneously, as one can make the type 1 error as small
as one pleases. In some cases, one cannot afford a type
1 error as large as .1, because the type 2 risk will be
too large. In other cases, on can afford .0001. This
range can come from a range of sample sizes for one
particular problem.
Now confidence intervals consider the various states of
nature, so what do they ignore? If the only consequence
considered bad is the parameter not being in the interval,
the whole line does an admirable job. So the size of the
interval has to be considered, and different sizes will
cause different levels to be used.
--
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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