Nrthugu

I'm using Cohen's d (implemented using cohen.d() from the effsize package) as a measure of effect size in my dependent variable between two levels of a factor.

My code looks like this: cohen.d(d, f) where d is a vector of numeric values and f is a factor with two levels: "A" and "B".

Based on my understanding, the sign of Cohen's d is dependent on the order of means (i.e. factor levels) entered into the formula. However, my cohen.d() command returns a negative value (and negative CIs), even if I reverse the order of levels in f.

Here is a reproducible example:

library('effsize')

# Load in Chickweight data

a=ChickWeight



# Cohens d requires two levels in factor f, so take the first two available in Diet

a=a[a$Diet==c(1,2),]

a$Diet=a$Diet[ , drop=T]



# Compute cohen's d with default order of Diet

d1 = a$weight

f1 = a$Diet

cohen1 = cohen.d(d1,f1)



# Re-order levels of Diet

a$Diet = relevel(a$Diet, ref=2)



# Re-compute cohen's d

d2 = a$weight

f2 = a$Diet

cohen2 = cohen.d(d2,f2)



# Compare values

cohen1

cohen2 

Can anyone explain why this is the case, and/or if I'm doing something wrong?

Thanks in advance for any advice!

I'm not entirely sure what the reasoning behind the issue in your example is (maybe someone else can comment here), but if you look at the examples under ?cohen.d, there are a few different methods for calculating it:

treatment = rnorm(100,mean=10)

control = rnorm(100,mean=12)

d = (c(treatment,control))

f = rep(c("Treatment","Control"),each=100)

## compute Cohen's d

## treatment and control

cohen.d(treatment,control)

## data and factor

cohen.d(d,f)

## formula interface

cohen.d(d ~ f)

If you use the first example of cohen.d(treatment, control) and reverse that to cohen.d(control, treatment) you get the following:

cohen.d(treatment, control)

Cohen's d



d estimate: -1.871982 (large)

95 percent confidence interval:

      inf       sup 

-2.206416 -1.537547 



cohen.d(control, treatment)

Cohen's d



d estimate: 1.871982 (large)

95 percent confidence interval:

     inf      sup 

1.537547 2.206416

So using the two-vector method from the examples with your data, we can do:

a1 <- a[a$Diet == 1,"weight"]

a2 <- a[a$Diet == 2,"weight"]

cohen3a <- cohen.d(a1, a2)

cohen3b <- cohen.d(a2, a1)

I noticed that f in the ?cohen.d examples is not a factor, but a character vector. I tried playing around with the cohen.d(d, f) method, but didn't find a solution. Would like to see if someone else has anything regarding that.