Them's pretty harsh words, David; and since I cannot see how your
subsequent words support the assertion, I'd be grateful if you would
explain. (The more especially as I expect to be addressing hypothesis
testing in the class I'm currently teaching, before the term is out;
and if I've been doing it wrong all this long while, it's probably about
time I were stopped before another generation of students is corrupted.)
On Wed, 24 Sep 2003, David Jones wrote:
> This is a total misconception of what is going on.
I had written (with rather more context than David quotes, but the
context was consistent with the quote):
> > The null hypothesis is the one that permits you to define a
> > sampling distribution for the statistic you will observe. A
> > distribution cannot be specified for an hypothetical inequality:
> > so the "null" hypothesis is always the one that contains an equals
> > sign (=).
David Jones replied as follows, with my responses embedded within this
copy of his post:
> This is a total misconception of what is going on. The presence of an
> equals sign has nothing to do with choosing the null hypothesis.
There may be a quibble to be had on whether we are discussing the choice
of a null hypothesis, or the syntax of writing about it after the choice
has been made. In the context of the original poster, there were two
hypotheses specified: {Mu < 150 psi} and {Mu >= 150 psi}. Given these
two, which is properly called the null?
(Now, one can argue -- as I would -- that these were not in fact the two
hypotheses the poster ought to have been discussing. But that is
another question -- the one identified as "(2)" in my reply to jjliu,
while in the material David quoted I was aiming at "(1)", rephrased in
the last sentence of the previous paragraph above ("Given these ...").)
> Possibly the "professor" is under the same misapprehension.
Mmm... Just what IS that misapprehension?
> Where one-sided tests are concerned, the "real" null hypothesis is a
> composite one
Yes, that follows from the one-sidedness, I had thought...
> and the critical point of the test statistic is chosen so that the
> probability of rejection satisfies a certain inequality for all point
> "null hypotheses" within the composite null hypothesis region (i.e.
> any given point null hypothesis is considered to be true and the
> probability of rejection is determined for this truth)... this leads
> to a point null hypothesis which is on the boundary effectively being
> the one which determines the critical point.
Yes: and is not the boundary between {Mu < 150 psi} and {Mu > 150 psi}
the hypothesis that {Mu = 150 psi} ? And is not this hypothesis stated
with an equals sign?
I'm sorry, and it is doubtless due to obtuseness on my part, but you
have not convinced me that my words were either "a total misconception
of what is going on" or "a misapprehension".
> As said in another post, the null hypothesis is the one which one is
> prepared to accept unless there is strong evidence to the contrary.
Yes. This speaks to choosing the direction of a one-sided hypothesis,
or in other terms the locus of the burden of proof. This point had been
explicitly acknowledged in my response to jjliu, as having been dealt
with by Duncan (Murdoch).
In case it may help the clarity of discourse, here are the two questions
as identified at the beginning of my response to jjliu:
==== DFB ==== DFB ==== DFB ==== DFB ==== DFB ==== DFB ==== DFB ====
There are two questions lurking here:
(1) Which is the null hypothesis and which the alternative?
(2) In which direction ought a one-sided hypothesis to be specified?
Duncan addressed (2); jjl's professor was dealing with (1):
==== DFB ==== DFB ==== DFB ==== DFB ==== DFB ==== DFB ==== DFB ====
-----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816
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