R/wilsonCI.R

In s-huebler/regsisF20: MATH 5573 Functions

#' Wilson Confidence Intervals for Binomial Estimate
#'
#' Calculates the alpha% confidence interval for a binomial estimate using the Wilson correction.
#'
#' @param x , number of successes
#' @param n , number of trials
#' @param alpha , alpha
#'
#' @return Confidence interval as a list of lowerbound, upperbound
#' @export
#'
#' @examples
#'  x=5; n=15; wilsonCI(x,n)
#'
wilsonCI<- function(x,n,alpha=0.05){
  z<-stats::qnorm(alpha/2)
  if (n==0){
    return ("Not Enough Samples")
  }
  x<- x/n
  discrim<-x*(1-x)/n+z^2/(4*n^2)
  if (discrim < 0 | x>1)
  {
    return ("Discriminant Less Than Zero")
  }
  Ci<- c((x+z^2/(2*n)-z*(sqrt(discrim)))/(1+z^2/n),(x+z^2/(2*n)+z*(sqrt(discrim)))/(1+z^2/n))
  Ci<-c(min(Ci), max(Ci))

  class(Ci)<-"confidenceInts"
  Ci
}