As always, Jim makes good points. Don't waste your time searching for
an example where a 1-alpha confidence interval includes zero effect but the
hypothesis test is significant at alpha, or where the confidence interval
does not include zero but the test is not significant. As Jim well knows,
you will not find such a case, and that, of course, is his point.
The CI approach may or may not be easier to teach, and may or may not
be less likely to be misinterpreted. Jim may well be correct that were we
to use confidence intervals instead of hypothesis tests the typical users
would find ways to screw up the interpretation of CIs every bit as much as
they now do with hypothesis tests. Sigh.
My point is that the CI gives you everything you get with the hypothesis
test and more.
Consider the following two possible outcomes:
A. p = .051, and a 95% CI for d runs from -0.135 to 8.5415.
B. p = .051, and a 95% CI for d runs from -.0002 to .0782.
These two possible outcomes paint very different pictures for me. When I
see outcome A, I think that the effect could be small in one direction or
enormous in the other direction, and I am motivated to do what it takes to
narrow the confidence interval (get more data, probably). When I see
outcome B, I am pretty well convinced that the effect is trivial in
magnitude, regardless of whether it is in this or that direction, and will
probably choose to treat it as nil (and I prefer Plavix to aspirin).
Cheers,
Karl W.
----- Original Message -----
From: "Jim Clark" <[EMAIL PROTECTED]>
Jim replies:
But we no longer report simply whether an effect is significant or not;
rather, we report the p value of the effect. I suspect that knowing
that p = .051 would be no more likely to be misinterpreted than the
confidence interval.
>>> [EMAIL PROTECTED] 24-Jun-05 2:12:28 PM >>>
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