Richard - If you forget about doing a hypothesis test and just consider the
question of how well you can approximate the cumulative distribution of a
binomal RV by that of a Normal, then you will see that the approximation is
better if you use the continuity correction.
By this argument, one would expect that in general, the test level should be
closer to the nominal level if you use the correction - but this is not a
proof. I would guess for some combinations of p n and k (# of successes)
it's possible that the error induced by not using the contiuity correction
would cancel the bias of the binomial test.
Al Feiveson
-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Richard
Williams
Sent: Friday, September 10, 2004 9:06 AM
To: [email protected]
Subject: st: prtest and the correction for continuity
As a sort of followup to my question about binomial confidence intervals
(you can tell what is coming up in my classes soon) -- In the single sample
case, -prtest- uses the normal approximation to the binomial, i.e. it
relies on the fact that, as the number of binomial trials in an experiment
increases, the distribution of the successes becomes more and more like a
normal distribution. However, it isn't really normally distributed,
because you can't have, say, 12.5 successes.
Some authors therefore recommend a correction for continuity -- if the
number of successes is more than hypothesized, you subtract .5; if less,
then you add .5.
-prtest- does not do the correction for continuity nor does it offer an
option for doing so. Is this because
(a) the correction has now come to be widely discredited, or
(b) nobody ever asked for it before?
I've seen several sources use the correction and several not use it. I
also get the impression that the correction is controversial because it
sometimes makes matters worse rather than better, but I'm not clear on what
those conditions are. Of course, it is best just to use the -bitest-
command, but if you had to use the normal approximation to the binomial,
should you apply the correction, or not? (Put another way, have I been
misleading my students for 15+ years by teaching the correction for
continuity?)
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
FAX: (574)288-4373
HOME: (574)289-5227
EMAIL: [email protected]
WWW (personal): http://www.nd.edu/~rwilliam
WWW (department): http://www.nd.edu/~soc
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