[R] ?Accuracy of prop.test

Rolf Turner rolf.turner at xtra.co.nz
Mon Jul 18 01:11:39 CEST 2011

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The Minitab and TI results are (modulo different levels of rounding)
just what you'd get from
doing the problem ``by hand'' in the good old-fashioned way. :-)

The Excel result appears to be the same with an excessive level of rounding.

The ``by-hand'' procedure uses the plug-in method to get an
approximation to the standard
error of p.hat.  The prop.test() function uses a more sophisticated
approach which involves
solving a quadratic equation to determine the endpoints of the
confidence interval.  This
more sophisticated solution is a pain in the pohutukawa ( :-) ) to
calculate by hand, but if you've
got a computer to do the nasty arithmetic for you, then why not?

The formula for the confidence interval endpoints using the more
sophisticated method can
be found e.g. in Jay L. Devore, Probability and Statistics for
Engineering and the Sciences,
Thomson --- Brooks/Cole, 6th ed., 2004, page 295. equation (7.10).  The
much simpler old-fashioned
formula is given on the same page as equation (7.11).

Presumably these formulae can be found in the Newcombe reference cited
in the help for
prop.test(); I haven't checked.

HTH

cheers,

Rolf Turner

On 18/07/11 04:27, Jack Sofsky wrote:
> I have just joined this list (and just started using R), so please
> excuse any etiquette breaches as I do not yet have a feel for how the
> list operates.
>
> I am in the process of teaching myself statistics using R as my
> utility as my ultimate goals cannot be satisfied by Excel or any of
> the plug-ins I could afford.
>
> I am currently looking at chap12 page 552 of Weiss's Introductory
> Statistics 9th edition.  Example 12.5 demonstrates using "Technology"
> to obtain a One-Proportion z-Interval.
>
> n=202
> x=1010
> confidence interval = .95.
>
> 0.175331, .224669
> .17533, .22467
> Answer given by Weiss's Excel Plug-in
> 0.175 < p < 0.225
>
> Here is what I got with R
> prop.test(202,1010,correct="FALSE")
>
>     1-sample proportions test without continuity correction
>
> data:  202 out of 1010, null probability 0.5
> X-squared = 363.6, df = 1, p-value < 2.2e-16
> alternative hypothesis: true p is not equal to 0.5
> 95 percent confidence interval:
>  0.1764885 0.2257849
> sample estimates:
>   p
> 0.2
>
> I'm also getting slight differences in the answers for exercises and
> find this disconcerting.
>
> Why are these differences present  (or am I doing something wrong)?

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