R/survey_size.R

In kamermanpr/surveytools: Miscellaneous tools for market research

#' Calculate the sample size of a survey.
#'
#' \code{survey_size} calculates the sample size of a survey based on user
#' imputs of margin of error, confidence level, response distribution, and
#' population size.
#'
#' @param error_margin The amount of error that can be tolerated, where the
#'   margin of error is how close the calculated value is to the “true
#'   value” for the population. The smaller the margin of error, the closer
#'   the calculated value will be to the "true value" at the specified
#'   confidence level. Defaults to 0.05 (5\%).
#' @param conf_level The amount of uncertainty that can be tolerated, where
#'   the confidence level is the certainty with which the sample accurately
#'   reflects the population, within the specified margin of error.
#'   Defaults to 0.95 (95\%).
#' @param response_distr The expected distribution of responses to a binary
#'   question. Defaults to 0.5: either answer is equally likely to be
#'   chosen.
#' @param population_size Estimated size of the population being surveyed.
#'   Defaults to NULL. The function produce an error if a \code{population_size} value is not specified.
#'
#' @return None
#'
#' @export
#'
#' @examples
#' \dontrun{
#' # Calculate sample size using the defaults
#' survey_size(population_size = 20000) # sample size = 377
#'
#' # Calculate the sample size required for a survey of a group of
#' # specialist physicians (population = 450), with a margin of error of
#' # 10%, and a confidence level of 99%. Assume the response distribution
#' # is 50%.
#' survey_size(error_margin = 0.1, conf_level = 0.99, population_size = 450)
#' # sample size = 121
#' }

survey_size <- function(sample_size = NULL,
                        error_margin = 0.05,
                        conf_level = 0.95,
                        response_distr = 0.5,
                        population_size = 100000) {
    e <- error_margin
    r <- response_distr
    N <- population_size
    n <- sample_size
    c <- conf_level
    z <- qnorm(1 - (1 - c)/2) # critical z-score for conf level (two tailed)

    if(is.null(N)){
        stop('Specify population size. See \'?survey_size\'', call. = TRUE)
    } else {
    x <- z^2 * r * (1 - r)
    numerator <- N * x
    denominator <- (N - 1) * e^2 + x
    sample_size <- round(numerator / denominator)

    sample_df <- data.frame('Parameter' = c('REQUIRED SAMPLE SIZE',
                                         'Population size',
                                         'Margin of error',
                                         'Confidence level',
                                         'Response distribution'),
                            'Value' = c(sample_size,
                                      N,
                                      e,
                                      c,
                                      r))
    }
    sample_df
}