Estimate Cohen's d for effect size

given two vectors:

x <- rnorm(10, 10, 1)
y <- rnorm(10, 5, 5)

How to calculate Cohen's d for effect size?

For example, I want to use the pwr package to estimate the power of a t-test with unequal variances and it requires Cohen's d.

Following this link and wikipedia, Cohen's d for a t-test seems to be:

Where sigma (denominator) is:

So, with your data:

set.seed(45)                        ## be reproducible 
x <- rnorm(10, 10, 1)                
y <- rnorm(10, 5, 5)

cohens_d <- function(x, y) {
  lx <- length(x) - 1
  ly <- length(y) - 1
  md <- abs(mean(x) - mean(y))        ## mean difference (numerator)
  csd <- lx*var(x) + ly*var(y)
  csd <- csd/(lx + ly)
  csd <- sqrt(csd)                     ## common sd computation
  cd <- md/csd                        ## cohen's d
  return(cd)
}

> res <- cohens_d(x, y)
> res
# [1] 0.5199662