On 15 Apr 2000, Donald F. Burrill wrote:
> > > (2) My second objection is that if the positive-discrete
> > > probability is retained for the value "0" (or whatever value the former
> > > "no" is held to represent), the distribution of the observed quantity
> > > cannot be one of the standard distributions. (In particular, it is not
> > > normal.) One then has no basis for asserting the probability of error
> > > in rejecting the null hypothesis (at least, not by invoking the standard
> > > distributions, as computers do, or the standard tables, as humans do
> > > when they aren't relying on computers). Presumably one could derive the
> > > sampling distribution in enough detail to handle simple problems, but
> > > that still looks like a lot more work than one can imagine most
> > > investigators -- psychologists, say -- cheerfully undertaking.
> >
> > This would not be a problem if the alternative was one-tailed, would it?
>
> Sorry, Bruce, I do not see your point. How does 1-tailed vs. 2-tailed
> make a difference in whatever the underlying probability distribution is?
>
Donald,
It was clear at the time, but now I'm not sure if I can see my
point either! I think what I was driving at was the idea that a point
null hypothesis is often false a priori. But if you have a one-tailed
alternative, then you don't have a point null, because the null
encompasses a whole range of values. For example, if your alternative is
that a treatment improves performance, then the null states that
performance remains the same or worsens as a result of the treatment. It
seems that this kind of null hypothesis certainly can be true. And I
think it is perfectly legitimate to use the appropriate continuous
distribution (e.g., t-distribution) in carrying out a test. Or am I
missing something?
Cheers,
Bruce
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