R/calc.n.binomial.R

In koenderks/auditR: A Multifunctional R Package for Auditing

#' Audit Sample Size for Large Samples
#'
#' This function calculates the required sample size for an audit, based on
#' the Binomial distribution. The Binomial distribution can be used if the
#' expected required sample is less than 10\% of the population.
#' \deqn{\frac{n}{N} < 0.10}{n / N < 10\%}
#'
#' @usage calc.n.binomial(expected.mistakes, materiality, confidence = 0.95)
#'
#' @param expected.mistakes An integer representing the number of expected mistakes
#' in the sample.
#' @param materiality A value representing the materiality of the audit in percentages.
#' @param confidence The amount of confidence desired from the bound
#' (on a scale from 0 to 1), defaults to 95\% confidence.
#'
#' @return A value indicating the required sample size for the audit.
#'
#' @section Details: EMPTY FOR NOW
#'
#' @author Koen Derks, \email{k.derks@nyenrode.nl}
#'
#' @seealso
#'
#' @references
#'
#' @examples
#' # Calculate the required sample size for a materiality of 5\% when one mistake
#' # is expected to be found in the sample.
#' calc.n.binomial(expected.mistakes = 1,
#'                 materiality = 0.05,
#'                 confidence = 0.95)
#'
#' @keywords sample size
#'
#' @export

calc.n.binomial <- function(expected.mistakes,
                            materiality,
                            confidence = 0.95){
  alpha <- 1 - confidence
  for(i in 1:2000){
    x <- choose(i, 0:expected.mistakes) * materiality^(0:expected.mistakes) *
          (1-materiality)^(i- (0:expected.mistakes))
    if(sum(x) < alpha)
      return(i)
  }
}