Michael Granaas wrote:
> 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.
The question is - why is one predicting it? If the situation where the
difference is 3 corresponds to some natural state of affairs - an obvious
model - then the deviation (mu1 - mu2) - 3 from that is naturally
considered
as an "effect".
And they will have an easier time
> understanding any implications of rejecting/not rejecting a hypothesis in
> the first case.
If the "3" is pulled out of empty air, yes. If the difference of 3 has
some source, the hypotheses can be phrased as (eg)
H0: being in the target population has no effect on sexual dimorphism in
height
Ha: being in the target population does affect sexual dimorphism in
height
which gets to the real heart of the matter.
> If Robert is saying it is not sensible to test (mu1 - mu2 = 3) under any
> circumstances I disagree.
No, I'm not saying that: that is the *same* as testing ((mu1 - mu2) - 3
= 0).
I am saying that if it makes sense to test that, the quantity mu1-mu2-3
should have some reasonable interpretation, so that the test can reasonably
be thought of as testing a "something=0" hypothesis.
> 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.
I'll concede this one freely. I'm not saying that every null hypothesis
of the form theta=0 is good - but I would suggest that most good null
hypotheses
can be cast into this form in a natural way. In other words, if it makes
sense
to test theta=theta_0, the difference theta - theta_0 ought to have some
natural
interpretation.
-Robert Dawson
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