Hedges's g variance and standard error from Cohen's d in R

Question

I need to calculate in R the variance and standard error based on the reported Cohen’s d value in a study. For instance, considering differences between two groups (n_group_1 = 25; n_group_2 = 25) that resulted in a Cohen’s d value of 0.58, I need three distinct values: (a) the value of Hedges' g; (b) the variance of Hedges' g; (c) and the standard error of Hedges' g. I appreciate your help!

Answer 1

Here are two functions to compute Hodges' g from Cohen's d. The functions' names could be improved upon.

# Cohen's d to Hedges' g
# Hedges' g computed from
# Cohen's d and sample sizes
d2g <- function(d, n1, n2 = n1) {
  n <- n1 + n2
  df <- n - 2L
  d/sqrt(n/df)
}
# Hedges' g standard error computed
# from Cohen's d and sample sizes
d2g_se <- function(d, n1, n2 = n1, var.equal = FALSE) {
  g <- d2g(d, n1, n2)
  if(var.equal) {
    sqrt(1/n1 + 1/n2)
  } else {
    sqrt( (n1 + n2)/(n1*n2) + g^2/(2*(n1 + n2)) )
  }
}

d2g(0.58, 25)
#> [1] 0.5682816
d2g(0.58, 25, 25)
#> [1] 0.5682816
d2g_se(0.58, 25, 25)
#> [1] 0.2884951
d2g_se(0.58, 25, 25, var.equal = TRUE)
#> [1] 0.2828427

^{Created on 2024-07-13 with reprex v2.1.0}