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Topic: CI for p
Replies: 1   Last Post: Apr 11, 1997 2:58 PM

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Richard Scheaffer

Posts: 440
Registered: 12/6/04
Re: CI for p
Posted: Apr 11, 1997 2:58 PM
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On CI's, the CI for p with p-hat in the variance is
too liberal in that it produces intervals for which
the coverage probability tends to be much smaller
than the nominal. For example, it is not unusual for
intervals of nominal 95% coverage to have actual
coverage probabilities more than 10% lower than that
even for samples as large as 30. Using the t
multiplier instead of the z makes the intervals a
little longer and, hence, increases the coverage
probability. Thus, the t turns out to be a decent
practical solution for no good theoretical
reason.

There are many other "solutions" to this problem,
some of the better ones coming out of the Bayesian
approach. But, it is difficult to bring all of this
into an introductory course. For AP, we will have to
accept the standard textbook approach.

A good resource is the book by Santner and Duffy
(1989), THE STATISTICAL ANALYSIS OF DISCRETE DATA,
Springer-Verlag.

Dick Scheaffer





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