My comments are about half-way down.
Michael
On Mon, 10 Apr 2000, Robert Dawson wrote:
> 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:
>
This (point 4) is certainly what we have been lead to believe, but I
question the assumption. Do we not in fact teach that we are to act as if
the null is true until we can demonstrate otherwise? I'm not sure where
this assumption came from (Fisher, someone's interpretation of Fisher,
someone other than Fischer) but there is no logical problem with assuming
something that might plausibly be true and using it as our null.
Isn't that what we do in our experiments all the time? We assume that our
experimental manipulation has no effect, which is plausibly true at least
for some time, and then we try to disprove that estimate of the effect.
Failing to do so we act as if the effect were absent (or so small as to be
absent for all practical purposes).
In many cases, however, we are only interested in the presense/absence of
an effect and this is plenty good enough. But, sometimes we want to
estimate, model, an effect. In this case we want a parameter estimate
that is reasonbly close to the population value for that effect. In this
case we might prefer confidence intervals or some such, but we could
certainly adopt our best estimate of the parameter and try to disprove it
by using it as the value tested in the null hypothesis.
There is no logical problem with adopting a plausibly true value for the
null and accepting it if it survives efforts to discredit it. That is
there is no logical problem with using a prediction approach.
> (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.
Yes. But, we can assume a genuinely true hypothesis as well as one that
is in all likelihood false. That does not pose any problem for the
computation of alpha levels.
The problem is that in too many cases our predictions of what is true are
too weak to allow point/narrow interval predictions of what is true. We
can only predict <> 0. In this case it seems that we are stuck with
rejecting a zero valued null in the correct direction as the strongest
form of theory confirmation that we have. Robert is correct, predicting
any particular value in this situation is arbitrary and pointless.
But, if the theory is strong enough to make narrow predictions those
should be used as the null and either disproved (rejected) or
corroborated (accepted).
>
> (7) Back at the beginning we wanted a yes-or-no answer. Henced fixed
> alpha testing and the pretence that we "accept" null hypotheses.
If the null is plausibly true we need no pretense. We accept the null as
true until something better comes along. I personally have accepted the
notion that psi powers do not exist despite the fact that all I have is a
string of failures to reject the null as evidence.
>
> 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.
Yes. Since I refuse to start with assumption that the null must be false
to be useful I end up in a somewhat different place.
>
> -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/
> ===========================================================================
>
*******************************************************************
Michael M. Granaas
Associate Professor [EMAIL PROTECTED]
Department of Psychology
University of South Dakota Phone: (605) 677-5295
Vermillion, SD 57069 FAX: (605) 677-6604
*******************************************************************
All views expressed are those of the author and do not necessarily
reflect those of the University of South Dakota, or the South
Dakota Board of Regents.
===========================================================================
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/
===========================================================================
