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

Confidence intervals for binomial proportions
---------------------------------------------

   ^propci^ [weight] [^if^ exp] [^in^ range] , ^c^ond^(^cond^)^  [^l^evel^(^#^)^
                ^none^ ^all^ ^ar^csin ^ew^ald ^ex^act ^wa^ld ^wi^lson ]

   ^propci ?^


^fweights^ are allowed; see help @weights@.


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

^propci^ computes the proportion of cases in which a Boolean condition (^cond^) is
true, and presents an associated confidence interval using zero or more of five
different methods.  The condition cond is used to define a temporary indicator
variable and the @tabulate@ command is then applied to calculate the proportion.

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


Options
-------

^cond(cond)^ provides a Boolean (true-false) expression that defines the propor-
    tion of interest (say, p = x/n).  ^[^Not optional.^]^

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

^all, none^ choose among the following confidence intervals in the obvious way.

^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.


Examples
--------

 . ^propci if !missing(sex), cond(upper(sex) == "M") lev(.975) ew ar^
 . ^propci if upper(sex) == "M", c((bodywt>200) & (bodywt!=.)) all lev(99)^
 . ^propci, c( (age > 60)|(age < 20) ) exact ewald^
 . ^propci, c( (age > 60) & (wt/ht > 2.5) ) arcsin^


Author
------

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


Also see
--------

 Manual:   ^[R] ci^
           ^[R] tabulate^
 On-line:  help for @bitest@, @ci@, @tabulate@, @propcii@