Yes, Paul, fair reading -- of course, in general, one should not ignore
the lower end of the CI, but in this case, they don't much differ between
examples.
In case A the CI suggests that we might have a large effect, but there
is a hulluva-lotta error in the estimate (very wide CI). In case B the CI
suggests that we can have great confidence in asserting that the effect is
very small, in one direction or the other. This, of course, can be a very
important conclusion, for example, for establishing the equivalence of two
treatments. I we altered the p in case B to .049, the difference would be
"significant" but, IMHO, we could still use the barely altered CI to assert
equivalence.
Karl W.
----- Original Message -----
From: "Paul Smith" <[EMAIL PROTECTED]>
To: "Teaching in the Psychological Sciences" <[email protected]>
Sent: Saturday, June 25, 2005 12:25 PM
Subject: Re: p = .051
Okay, that does clarify things quite a bit for me. If I'm reading your
argument correctly, you're saying that the difference between the two
examples in the upper ends of the CIs (8.5415 versus .0782) does a
better job of illustrating the differences between the examples than
does the difference in effect sizes (.039 versus 4.25). Is that a fair
reading? (oh, and the p-value itself isn't really adding much of
anything, is it?).
Paul Smith
Karl L. Wuensch wrote:
> Here are more details on the hypothesis test of no effect, which for
> the
> sophisticated reader will provide the same information provided by the
> confidence interval on d, but, IMHO, not for the naive reader (that is,
> most
> consumers of and many producers of behavioral research).
>
> A. n1 = 2, n2 = 2, t(2) = 4.25, p = .0512. Using the SPSS script at
> http://core.ecu.edu/psyc/wuenschk/SPSS/CI-d-SPSS.zip or the SAS program at
> http://core.ecu.edu/psyc/wuenschk/SAS/Conf-Interval-d2.sas , g (point
> estimate of Cohen's d) = 4.25 and a 95% confidence interval on d runs
> from -.0135 to 8.5415. Yes, I purposely chose a small sample size and a
> big
> point estimate of effect, better to illustrate my point.
>
> B. n1 = 5000, n2 = 5000, t(9998) = 1.95, p = .0512, g = .039, and the
> confidence interval for d runs from -.0002 to .0782.
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