I, and I think Dennis, are arguing that when we test a hypothesis we
should have a null hypothesis that is plausibly true. A hypothesis that
reflects some sort of an effect size estimate where such an estimate is
meaningful.
If I understand correctly Robert is arguing that we should always phrase
the null so that it becomes a hypothesis of no effect.
In one case we can do that mathematically by rearranging a hypothesis of
(mu1 - mu2 = 3) to the form ((mu1 - mu2) - 3 = 0). If this is what Robert
means by saying that only no effect hypotheses are meaningful I think we
are in partial agreement. I personally shudder to think of trying to
teach the second form to my students. I think that they will have a much
easier time understanding that I am predicting a difference between two
groups of 3 units using the first. And they will have an easier time
understanding any implications of rejecting/not rejecting a hypothesis in
the first case.
If Robert is saying it is not sensible to test (mu1 - mu2 = 3) under any
circumstances I disagree.
My reading of another message is that he thinks there should be some prior
evidence for testing a hypothesis of 3 units of difference. If my reading
here is correct I think that we may be differing in what we consider
adequate prior evidence, but otherwise are close.
I guess I don't wish to argue all three possibilities if only one of them
is an actual point of disagreement.
For reasons I am willing to develop fully later I think that specifying a
plausibly true value for a null hypothesis (test hypothesis) is more
valuable than a null hypothesis where the specified value is not plausibly
true.
In psychology, and I think education, we see the zero value specified when
it is not even remotely plausible way too often. This plausibility
judgement is informed by at least some prior evidence.
By plausibly true I am willing to conceed some reasonable interval around
the tested null value where the interval size is informed by content area
knowledge. (I am willing to say that some small effects should be treated
as if they were zero. I am willing to say that true values only slightly
different from the hypothesized value should be treated as if they were
the hypothesized value.)
Michael
*******************************************************************
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.
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