{smcl}
{* 08sep2004}{...}
{hline}
help for {hi:bincoverage}
{hline}

{title:True coverage probabilities for binomial confidence intervals}

{p 8 12 2}{cmd:bincoverage}
    [{cmd:,} {cmd:n(}{it:#}{cmd:)} {cmd:p(}{it:#}{cmd:)}
    {cmdab:l:evel:(}{it:#}{cmd:)}
    {cmdab:exa:ct} {cmdab:w:ilson} {cmdab:a:gresti} {cmdab:j:effreys}]{break}

{title:Description}

{p 4 4 2}
{cmd:bincoverage} calculates true coverage probabilities for various binomial
confidence intervals, the Clopper-Pearson ({cmd:exact}) interval, the 
Wilson ({cmd:wilson}) interval, the Agresti ({cmd:agresti}) interval, and 
the Jeffreys ({cmd:jeffreys}) interval. 

{p 4 4 2}
For a given binomial experiment with {it:n} trials and probability of success
{it:p} for each trial, coverage probabilities are obtained by first
determining the set of binomial outcomes (from the set 0,1,...,{it:n}) 
resulting in confidence intervals which cover {it:p}.  The coverage probability
is then simply the sum of the binomial({it:n},{it:p}) density over these
outcomes.

{title:Options}

{p 4 8 2}{cmd:n(}{it:#}{cmd:)} specifies {it:n}, the number of Bernoulli 
trials.  By default, {it:n} is 10.

{p 4 8 2}{cmd:p(}{it:#}{cmd:)} specifies {it:p}, the success probability of 
each trial.  By default, {it:p} is 0.5.

{p 4 8 2}{cmd:level(}{it:#}{cmd:)} specifies the confidence level, in percent,
for confidence intervals; see help {help level}.

{p 4 8 2}
{cmd:exact}, {cmd:wilson}, {cmd:agresti}, and {cmd:jeffreys}
    specify how the binomial confidence intervals are to be calculated.
    At most one may be specified.

{p 8 8 2}
    {cmd:exact} is the default and specifies exact binomial confidence
    intervals.

{p 8 8 2}
    {cmd:wilson} specifies calculation of the Wilson confidence intervals.

{p 8 8 2}
    {cmd:agresti} specifies calculation of the Agresti-Coull confidence
    intervals.

{p 8 8 2}
{cmd:jeffreys} 
    specifies calculation of the Jeffreys confidence intervals.

{p 8 8 2}
    See Brown, Cai, and DasGupta (2001) for a discussion and comparison 
    of the different confidence intervals.

{title:Examples}

    {cmd:. bincoverage, n(100)}
    {cmd:. bincoverage, n(500) p(0.3) wilson}
    {cmd:. bincoverage, n(500) p(0.2) agresti level(90)}

{title:References}

{p 4 8 2}
Brown, L.D., T.T. Cai, and A. DasGupta.  2001.
    Interval estimation for a binomial proportion,
    {it:Statistical Science} 16: 101{c -}133.

{title:Also see}

    Manual:  {hi:[R] ci}

{p 4 13 2}
Online:  help for {help ci}.