Estimate Cohen's d for effect size

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

There are several packages providing a function for computing Cohen's d. You can for example use the cohensD function form the lsr package :

library(lsr)
set.seed(45)
x <- rnorm(10, 10, 1)
y <- rnorm(10, 5, 5)
cohensD(x,y)
# [1] 0.5199662

Another option is to use the effsize package.

library(effsize) 
set.seed(45) x <- rnorm(10, 10, 1) 
y <- rnorm(10, 5, 5) 
cohen.d(x,y)
# Cohen's d
# d estimate: 0.5199662 (medium)
# 95 percent confidence interval:
#        inf        sup 
# -0.4353393  1.4752717