Michael Granaas wrote:
> My grandmother could have told me that the mean height for men and women
> was not the same (zero difference). So based on prior evidence I
> hypothesize that the actual difference is 3 inches (mu1 - mu2 = 3) and use
> that for my null hypothesis. True, I can reduce this to a zero difference
> version by using (mu1 - mu2) - 3 = 0 but do I really want to?
if the 3" is credible enough to be worth testing, then yes, you do.
Example: 3" is determined from historical large-sample measurements to be
the difference for the population overall, and you want to determine whether
there is a larger difference in heights within male and female members of a
certain ethnic group; or you want to see if the height difference is
decreasing over time; or whether it is larger for the armed forces. In these
cases (mu1-mu2-3) represents "change in height difference explained by..."
and it is indeed the effect size.
However, if you are simply studying height differences, and do not have
any real source for that 3" figure, you would not be justified in pulling it
out of thin air just to permit you to do a hypothesis test. I would suggest,
in fact, that a very good rule of thumb would be that if you _can't_ cast a
null hypothesis meaningfully in the form "effectsize = 0" you should be
very, very wary of doing the test at all.
-Robert Dawson
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