San wrote:
>
> Would there be some cases which the p-value are so difficult to find
> that it's nearly impossible?
I'm tempted to say "not under a randomization model" but, yes, there
are many problems for which P values are not readily available.
Perhaps P values are unavailable for *most* problems--it's just that
we're so good at figuring out new uses for the cases we can solve!
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.
> Is this a kind of limitation to the
> hypothesis testing using p-value?
Yes. Stepwise procedures (regression, in particular) are good
examples.
> Is there any substitute for the
> p-value?
Many. You could start with likelihood procedures, Bayes methods,
and decision theory.
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