R/sample.size.R

In mrdwab/mrdwabmisc: Miscellaneous R functions, mostly for data processing

#' Determine the Optimal Sample Size for a Given Population
#' 
#' The sample.size function either calculates the optimum survey sample size
#' when provided with a population size, or the confidence interval of using a
#' certain sample size with a given population. It can be used to generate
#' tables (data.frames) of different combinations of inputs of the following
#' arguments, which can be useful for showing the effect of each of these in
#' sample size calculation.
#' 
#' 
#' @param population The population size for which a sample size needs to be
#' calculated.
#' @param samp.size The sample size. This argument is only used when
#' calculating the confidence interval, and defaults to \code{NULL}.
#' @param c.lev The desired confidence level. Defaults to a reasonable 95\%.
#' @param c.int The confidence interval. This argument is only used when
#' calculating the sample size. If not specified when calculating the sample
#' size, defaults to 5\% and a message is provided indicating this; this is
#' also the default action if \code{c.int = NULL}.
#' @param what Should the function calculate the desired sample size or the
#' confidence interval? Accepted values are \code{"sample"} and
#' \code{"confidence"} (quoted), and defaults to \code{"sample"}.
#' @param distribution Response distribution. Defaults to 50\%
#' (\code{distribution = 50}), which will give you the largest sample size.
#' @note From a teaching perspective, the function can be used to easily make
#' tables which demonstrate how the sample size or confidence interval change
#' when different inputs change. See the "Advanced Usage" examples. The
#' following formulae were used in this function:
#' 
#' \deqn{\large ss = \frac{-Z^2\times p\times(1-p)}{c^2}}{% ss = (-Z^2 * p * (1
#' - p))/(c^2)}
#' 
#' \deqn{\large pss = \frac{ss}{1+\frac{ss-1}{pop}}}{% pss = ss/(1 + ((ss -
#' 1)/pop))}
#' @author Ananda Mahto
#' @references \itemize{ \item See the 2657 Productions News site for how this
#' function progressively developed:
#' \url{http://news.mrdwab.com/2010/09/10/a-sample-size-calculator-function-for-r/}
#' \item The \code{sample.size} function is based on the following formulas
#' from the Creative Research Systems web page \emph{Sample size formulas for
#' our sample size calculator}: \url{http://www.webcitation.org/69kNjMuKe} }
#' @examples
#' 
#' # What should our sample size be for a population of 300?
#' # All defaults accepted.
#' sample.size(population = 300)
#' 
#' # What sample should we take for a population of 300
#' #   at a confidence level of 97%?
#' sample.size(population = 300, c.lev = 97)
#' 
#' # What about if we change our confidence interval?
#' sample.size(population = 300, c.int = 2.5, what = "sample")
#' 
#' # What about if we want to determine the confidence interval
#' #   of a sample of 140 from a population of 300? A confidence
#' #   level of 95% is assumed.
#' sample.size(population = 300, samp.size = 140, what = "confidence")
#' 
#' ## ========================================= ##
#' ## =========== ADVANCED USAGE ============== ##
#' 
#' # What should the sample be for populations of 300 to 500 by 50?
#' sample.size(population=c(300, 350, 400, 450, 500))
#' 
#' # How does varying confidence levels or confidence intervals
#' #   affect the sample size?
#' sample.size(population=300,
#'        c.lev=rep(c(95, 96, 97, 98, 99), times = 3),
#'        c.int=rep(c(2.5, 5, 10), each=5))
#' 
#' # What is are the confidence intervals for a sample of
#' #   150, 160, and 170 from a population of 300?
#' sample.size(population=300,
#'        samp.size = c(150, 160, 170),
#'        what = "confidence")
#' 
#' @export sample.size
sample.size <- function(population, samp.size = NULL, c.lev = 95, 
                        c.int = NULL, what = "sample", distribution=50) {
  z = qnorm(.5+c.lev/200)
  
  if (identical(what, "sample")) {
    if (is.null(c.int)) {
      c.int = 5
      
      message("NOTE! Confidence interval set to 5.
      To override, set >> c.int << to desired value.\n")
      
    } else if (!is.null(c.int) == 1) {
      c.int = c.int
    }
    
    if (!is.null(samp.size)) {
      message("NOTE! >> samp.size << value provided but ignored.
      See output for actual sample size(s).\n")
    }
    
    ss = (z^2 * (distribution/100) * 
      (1-(distribution/100)))/((c.int/100)^2)
    samp.size = ss/(1 + ((ss-1)/population))    
    
  } else if (identical(what, "confidence")) {
    if (is.null(samp.size)) {
      stop("Missing >> samp.size << with no default value.")
    }
    if (!is.null(c.int)) {
      message("NOTE! >> c.int << value provided but ignored.
      See output for actual confidence interval value(s).\n")
    }
    
    ss = ((population*samp.size-samp.size)/(population-samp.size))
    c.int = round(sqrt((z^2 * (distribution/100) * 
      (1-(distribution/100)))/ss)*100, digits = 2)
    
  } else if (what %in% c("sample", "confidence") == 0) {
    stop(">> what << must be either -sample- or -confidence-")
  }
  
  RES = data.frame(population = population,
                   conf.level = c.lev,
                   conf.int = c.int,
                   distribution = distribution,
                   sample.size = round(samp.size, digits = 0))
  RES
}