R/percent_overlap.R

In pgrugwiro/variant: Quantifying Dataframe Changes

#' Confidence Interval Overlap Percentage
#'
#'
#' The percent_overlap() function is used to calculate the overlap percentage between
#' two numeric vectors. The function uses equation 3 described in chapter 2.
#' The function takes as input two numeric vectors and a desired level of significance and it
#' outputs the percentage overlap between the confidence intervals of population means of the
#' input vectors. If there’s no overlap of the confidence intervals, e.g., the upper bound of
#' the confidence interval of one vector is lower than the lower bound of the confidence
#' interval of the other vector, a negative percent overlap would be displayed.
#'
#'
#' @param x a numeric vector
#' @param y a numeric vector
#' @param alpha level of significance
#'
#' @return percentage overlap between the confidence intervals of the two numeric vectors
#' @export
#'
#' @examples
#'
#' \dontrun{vecx <- rnorm(100)
#' vecy <- rnorm(100)
#' percent_overlap(vecx, vecy, 0.05)}
#'
#'
percent_overlap <- function(x, y, alpha){
  z <- qnorm(1-alpha/2)
  K <- 1+ (sd(x)/sqrt(length(x)))/(sd(y)/sqrt(length(y)))
  if (mean(x) - mean(y) >= 0){
    omega <- (z*sd(y)*K/sqrt(length(y)) - (mean(x)-mean(y)))*100/(z*sd(y)*K/sqrt(length(y)) + (mean(x)-mean(y)))
  } else {
    omega <- (z*sd(y)*K/sqrt(length(y)) - (mean(y)-mean(x)))*100/(z*sd(y)*K/sqrt(length(y)) + (mean(y)-mean(x)))
  }
  return(omega)
}