----- Original Message -----
From: Ting Ting <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, October 13, 2000 10:57 PM
Subject: Re: questions on hypothesis
> >
> > A good example of a simple situation for which exact P values are
> > unavailable is the Behrens-Fisher problem (testing the equality of
> > normal means from normal populations with unequal variances). Some
> > might say we have approximate solutions that are good enough.
.................................................................
I see this as an imprecise statement of a hypothesis.
>From set theory, I can see several different logical constructs, each of
which would arrive at a different probability distribution, and consequently
different p values. It boils down to just what is the hypothesis on the
generator of the data. Is it a statement of logical equality or the value of
a difference function.
Does sample "A" come from process "a" and sample "B" come from process "b",
or do both samples come from process "c"?
The problem is simplified when process "a" and process "b" are known. When
process "a" and "b" are not known, we have that Fisher problem of defining a
set of all "a" parameter values <= to a given p1 value and defining a set of
all "b" parameter values <= to a given p2 value. When the processes are one
parameter processes, every thing is straightforward. (Fisher in his book-set
very nicely used one parameter distributions to illustrate his ideas.)
However for a two parameter process, the Fisher-Berens problem states an
equality (intersection) of mean values and a disjoint of variance values,
which cannot be analytically combined (given the normal distribution
function) in terms of a single p value.
Consequently, one finds in the textbooks, all the different approaches to
establish a "c" process, for which tests can be constructed to determine if
"A" and "B" come from the process "c" or not. The hypothesis being tested is
then based on process "c", not on the original idea.
DAH
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