R/prop.ci.R

In bgupsych/bgupsych: Useful commands for BGU Psychology students

#' Proportion Confidence Interval
#' @export
#' @param n is population size.
#' @param k is number of success.
#' @param conf is confidence level desired. default at 95.
#' @seealso \code{\link{prop.sig}} for a proportion significance test
#' @examples prop.ci(n=100,k=30)
#' prop.ci(100,30,conf=99)
#' @note  Calculates the binomal to normal assumption: \code{p&q * n > 5}.
#' @returns \code{p} Is the succses rate, given \code{n} and \code{k}.
#' @returns \code{q} Is the opposite probability of p (\code{1-p}).
#' @return \code{SE} The Standard Error estimate based on empirical observations (\code{p and q}).
#' @return \code{Lower} and \code{Upper} are the margins of the confidence interval.
#' @return \code{conf} is the confidence level.
#' @return \code{binom2norm} answers whether the assumption of normality is met.
prop.ci <- function(n,k,conf=95){
  p <- k/n
  q <- 1 - p
  Zscore <- qnorm((1 - conf/100)/2)
  seest <- sqrt((p * q)/n)
  norma <- p * n & q * n > 5

  return(data.frame(p = round(p, 3),
                    q = round(q, 3),SE = round(seest,3),
                    Lower = round(p + Zscore * seest, 3),
                    Upper = round(p - Zscore * seest, 3),
                    conf = round(conf),
                    binom2norm = ifelse(norma, "YES", "NO")))
}