.-
help for ^propcii^                                                [STB-52: sg119]
.-

Confidence intervals for binomial proportions (immediate)
---------------------------------------------------------

   ^propcii^ n x  [ , ^l^evel^(^#^)^ ^all^ ^ar^csin ^ew^ald ^ex^act ^wa^ld ^wi^lson ]

   ^propcii ?^


Description
-----------

^propcii^ accepts a sample size (^n^) and a binomial count (^x^) and computes the
proportion p = x/n, along with an associated confidence interval using any of
five different methods.  The command ^propcii n x^ is analogous to ^cii n x^, ex-
cept that four additional confidence interval methods are available.

The second syntax above displays a brief reminder of the first syntax.


Options
-------

^level(#)^ specifies the desired confidence level.  May be fractional and may be
    specified as a percentage (97.5) or a proportion (.9633).

^all^ chooses each of the following confidence intervals.

^arcsin^ produces an endpoint-adjusted, enhanced version of the classic arcsine
    transform-based interval.

^ewald^ gives an endpoint-adjusted, enhanced version of the classic normal theory
    (^Wald^) interval; see ^wald^, below.

^exact^ computes the Clopper-Pearson so-called "exact" confidence interval, the
    method used by the @ci@ and @cii@ commands.  (This is the default.)

^wald^ requests the classic normal theory interval, p +/- z*sqrt(p(1-p)/n), named
    for its connection with the Wald test; the limits here are endpoint-adjust-
    ed, as are those for all other methods.  (^ewald^ gives an "enhanced" version
    of the ^wald^ interval.)

^wilson^ yields an endpoint-adjusted interval that replaces the observed propor-
    tion, p = x/n, with Wilson's estimator, (x+2)/(n+4).


Notes
-----

In all cases above, "enhanced" means that the proportion p = x/n is judiciously
biased toward 1/2, so as to improve the minimum coverage probability of the re-
sulting interval.  For details of the enhanced arcsine (^arcsin^) and enhanced
Wald (^ewald^) intervals, as well as the details of "endpoint-adjustment," see:

    Gleason, J. R. (1999).  Better approximations are even better for interval
        estimation of binomial proportions.  Submitted for publication.

For details of the ^wilson^ confidence interval, see:

    Agresti, A. and Coull, B. A. (1998). Approximate is better than "exact" for
        interval estimation of binomial proportions. ^The American Statistician^,
        52, 119-126.

^propcii^ is the immediate form of, and is called by @propci@.


Examples
--------

 . ^propcii 23 3, lev(.975) all^
 . ^propcii 183 0, ewald arcsin level(99)^


Author
------

   John R. Gleason, Syracuse University, Syracuse NY, USA
   (loesljrg@@accucom.net)    [This is Version 1.0.1 (10Sep1999).]


Also see
--------

 Manual:   ^[R] cii^
           ^[R] tabulate^
 On-line:  help for @bitest@, @cii@, @tabulate@, @propci@