R/differences.R

In samuelfranssens/rlibrary: library with functions that I often use

#' A function that takes two means, sd's, n's and gives lower and upper bounds for estimated difference and cohen d
#'
#' This function will give you a confidence interval around a difference and its associated cohen's d
#'
#' formula for d = (mu1 - mu2) / sigma
#' where sigma = sqrt ( a / b ) = pooled standard deviation
#' where a = (n-1) x s1 x s1 + (n-2) x s2 x s2
#' where b = n1 + n2 - 2
#'
#' also: t = ( mean(x1) - mean(x2) ) / (sigma  * sqrt(1/n1 + 1/n2))
#' so t = d * 1 / sqrt(1/n1 + 1/n2)
#' so d = t * sqrt(1/n1 + 1/n2)
#'
#' @param mean1 mean 1
#' @param mean2 mean 2
#' @param sd1 sd 1
#' @param sd2 sd 2
#' @param n1 sample size 1
#' @param n2 sample size 2
#' @param alpha alpha level
#' @keywords effect size
#' @export
#' @examples
#' differences(mean1, mean2, sd1, sd2, n1, n2)

differences <- function(mean1, mean2, sd1, sd2, n1, n2, alpha = 0.95) {

  difference <- mean1 - mean2
  df <- n1+n2-2
  sd.pooled <- sqrt(( sd1*sd1 * (n1-1) + sd2*sd2 * (n2-1))/(df))

  lwr <- difference + qt((1-alpha)/2, df = df) * sd.pooled * sqrt(1/n1 + 1/n2)
  upr <- difference + qt((1+alpha)/2, df = df) * sd.pooled * sqrt(1/n1 + 1/n2)

  d.est <- difference / sd.pooled

  d.conf <- cohend(d.est,n1,n2) # requires the cohend function

  pvalue <- round(2 * pt( -abs( d.est / sqrt(1/n1+1/n2)  ), df=df), 4)

  # return:
  tibble(difference = difference,
         lwr = lwr, upr = upr,
         df = df, p = pvalue,
         d.est = d.est, d.lwr = d.conf[1], d.upr = d.conf[2])
}