Laura,
I would make the argument that continuity correction should not be used in
practice, or in the classroom. Continuity corrected intervals are, on average,
to wide. This might be defensible if they guaranteed their coverage level (as
'exact' distribution based intervals do), but due to the fact that they are
asymptotic, they may have coverage less than the nominal level.
The Agresti reference Ralph sent is an excellent article. I highly recommend
it. I find it helpful to categorize discrete tests on two axes. conservative
vs. approximate, and asymptotic vs distribution based. Conservative tests
attempt to keep type 1 error less than the nominal level, and approximate tests
attempt to keep the error near its nominal level.
Asymptotic
Distribution based
Conservative Continuity Corrected Standard 'Exact' test
Approximate Standard Asymptotic Mid p-value
I would also be interested to hear why the default it correct=TRUE. Perhaps it
is historical.
Ian
On Oct 25, 2010, at 1:38 PM, Laura Chihara wrote:
> Hi,
>
> I have a question about prop.test in R:
>
> I teach students the score confidence
> interval for proportions (also called
> Wilson or Wilson score interval).
>
> prop.test(,..., correct=FALSE) gives this
> interval.
>
> The default uses a continuity correction.
> When should we use one over the other?
> Is it worth going over this in class? Why
> is correct=TRUE the default?
>
> Thanks for any pedagogical guidance here!
>
> -- Laura
>
> *******************************************
> Laura Chihara
> Professor of Mathematics 507-222-4065 (office)
> Dept of Mathematics 507-222-4312 (fax)
> Carleton College
> 1 North College Street
> Northfield MN 55057
>
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