Estimate Cohen's d for effect size

Question

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.

Answer 1

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