On Mon, 10 Apr 2000, dennis roberts wrote in part:
> .. the fact that we create a null and test a null does NOT imply that
> we are therefore testing some effect size ...
Of course not. One does not TEST an effect size, one ESTIMATES it.
And it is useful to do so only if one has found it not equal to some
value (possibly, but not necessarily, zero) that would imply the effect
size to be uninteresting. (Sometimes it is convenient to do both of
these things at once, as in constructing a confidence interval. But
if the interval includes values that are, a priori, uninteresting, there
is little utility to pursuing the current estimate of the effect size.)
> and, if we were interested in an effect size, then we don't have to
> test for it ... but we could ask the question: how large is it? that is
> NOT a test of a hypothesis
>
> we don't need ANY null to find answers to questions of import that we
> might have
I beg to differ. Strenuously. The whole point of a point null
hypothesis is to be able to specify a probability distribution against
which one can assert, more or less credibly, that one's conclusion is
supported with a suitably limited probability of error. (Error, that
is, in drawing the conclusion.) For this reason Lumsden used to call
this the "model-distributional" hypothesis, which had the virtue of
describing its proper purpose moderately clearly, and had the obvious
defect of being too much of a mouthful for us ordinary folks to use in
conversation (or in classrooms, or in other contexts beginning with "c").
So long as the logical style of scientific argumentation is argument by
elimination, one needs a set of propositions about the world [Note: not
about the present sample, nor about statistics measured on the sample.]
that are both exhaustive and mutually exclusive (viz., the null and
alternative hypotheses), and a means of determining either that one
proposition is false, or that one's decision that it is false (should
one come to that decision) has a low probability of being wrong.
THAT is what hypothesis testing is about; and it follows that sensible
discussions of the form and/or values associated with a
model-distributional hypothesis cannot take place in the absence of the
alternative hypothesis(-es) that are to be considered simultaneously.
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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