R/CI.R

In IyarLin/hype: Variuos functions for proportions difference hypothesis testing

#' @title Calculate proportion difference confidence interval
#' @description this function calculates the proportion difference confidence interval.
#' This interval has probability alpha of containing the real difference.
#'
#' @param p_1_hat estimated population 1 p parameter
#' @param n_1 population 1 sample size
#' @param p_0_hat estimated population 0 p parameter
#' @param n_0 population 0 sample size
#' @param alpha confidence interval significance level
#' @param h number of hypothesis tested in the same experiment (for Bonferroni correction)
#'
#' @importFrom stats qnorm
#' @export
#'
#' @return a data.frame with 2 columns:
#'   \item{lower_bound}{confidence interval lower bound}
#'   \item{upper_bound}{confidence interval upper bound}
#' @example inst/CI_example.R
#'

CI <- function(p_1_hat, n_1, p_0_hat, n_0, alpha, h) {
  # validate inputs
  if (h != round(h) | h < 1) stop("h must be a positive integer")

  point_estimate <- p_1_hat - p_0_hat
  rhs <- qnorm(1 - alpha / (2 * h)) * sqrt(p_1_hat * (1 - p_1_hat) / n_1 + p_0_hat * (1 - p_0_hat) / n_0)

  ans <- data.frame(
    lower_bound = point_estimate - rhs,
    upper_bound = point_estimate + rhs
  )
  return(ans)
}