Dennis Roberts wrote:
> now we get to the crux of the matter ... WHY do we need a null ... or any
> hypothesis ... (credible and/or sensible) to test??? what is the
scientific
> need for this? what is the rationale within statistical exploration for
this?
My understanding, not perhaps parallelling the historical development
very closely, is that the answer is something like this. I'm sure somebody
will correct me...
(0) People want to be able to make qualitative statements: "Manure makes
the roses grow." "Electric shocks make mice do what you want them to." "If
I buy kippers it will not rain."
(1) In an attempt to be more scientific, instead of making absolute
statements, people decide to use the idea of probability. They would _like_
to be able to say "There is a 99% probability that if you put manure on
roses they will grow better." However, that does not fit in with
traditional frequency-based probability, which only officially assigns
probabilities to events which are "random", a phrase usually undefined or
defined only inductively "You know, dice, urns, all that stuff." Roses are
not random because you do not get to bet on them at Las Vegas. (Horses are
dubious. Few people recommend using the outcome of the 2:30 to assign mice
to treatment groups. )
(2) If there is going to be a probability involved, then, it has to
involve the sampling technique, as that is the only place where the
experimenter can introduce (or pretend to) an urn or pair of dice.
(3) Even given randomization via sampling, we need to know how things
really are to compute a probability. If we *did* know this we wouldn't be
doing statistics. But we can make a "conditional" statement that _if_
something were true then the probability of observing something would be....
(4) In order to avoid circular logic, we *cannot* assume what we want to
prove, in order to compute the probability. We can however assume it for a
contradiction. Therefore:
(5) There is some set of observations that will lead us to declare that
that contradiction is reached, and others that won't. Hence the rejection
region.
(6) The only definite outcome is rejecting the hypothesis, the only
situation in which we can compute the probability is when the hypothesis is
true. Hence alpha.
(7) Back at the beginning we wanted a yes-or-no answer. Henced fixed
alpha testing and the pretence that we "accept" null hypotheses.
OK, it's a horrible kludge at best, and an evil ritual at worst; but
*if* you start with those assumptions & goals, there's what comes out.
-Robert Dawson
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
