R/tools_borrowed_functions.R

In rcalinjageman/esci2: Effect Sizes and Confidence Intervals

# This function calculates the mean, sd, and n from multiple groups combined
# from summary data It was developed from an explanation found here:
# https://www.statstodo.com/CombineMeansSDs_Pgm.php
esci_combine_groups <- function(means, sds, ns) {
  
  vars <- sds^2
  dfs <- ns - 1
  
  sum_xs <- means * ns
  sum_vars <- vars*dfs +  sum_xs^2/ns
  
  total_n <- sum(ns)
  total_sum_xs <- sum(sum_xs)
  total_sum_vars <- sum(sum_vars)
  
  n <- total_n
  m <- total_sum_xs / total_n
  s <- sqrt((total_sum_vars-total_sum_xs^2/total_n) / (total_n-1)) 
  
  res <- list(
    m = m,
    s = s,
    n = n
  )
  
  return(res)
  
}