Michael Granaas wrote (in part):
> The problem is that interval estimation and null hypothesis testing are
> seen as distinct species. An interval that includes zero leads to the
> same logical problems as failure to reject a false null.
No; an interval that includes zero has additional information. Not
(to open another can of worms) because of being a confidence interval;
we can construct a 95% confidence region, the union of two intervals,
consisting of precisely the *least* plausible values, and it is possible
to construct a 95% CI that contains no information whatsoever about the
value of the parameter! But as somebody (Kalbfleisch? George Gabor?) said
once, the reason that confidence intervals as usually computed work as well
as they do is that they are closely related to maximum-likelihood intervals.
I'm afraid that I don't follow your definition of a "plausible null".
On the one hand, you say that my value (in the simulation I included) of
102 for the mean IQ of a population is "a priori false"; you then say that
"I like interval estimates because they give me a good
range for my plausibly true values for the null."
But if I had computed a 95% confidence interval from almost any of those
simulated data sets, 102 would have been in it.
Had I said that the mean IQ was actually 102 and that I was testing
the null hypothesis that it was 100, would you have called _that_ a
plausible null? My point - that repeated failures to reject the null
should *not* automatically increase one's belief in its truth - would
be equally valid.
-Robert Dawson
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