How to Calculate Cohen’s d in R

In this article, we will discuss what is Cohen’s d and how to Calculate Cohen’s d in R Programming Language.

What is Cohen’s d?

Cohen’s d is a measure that indicates the difference between two means. It is commonly used to quantify the magnitude of the difference between two groups in a study.

It is described Mathematically as

[Tex]Cohen’s d = \frac{x_1 – x_2}{\sqrt{\frac{s_1^2 + s_2^2}{2}}} [/Tex]

where:

• x₁, x₂: mean of both samples
• s₁², s₂²: variance of both samples

Interpretation of Cohen’s d

1. Small size effect: 0.2 ≤ Cohen’s d < 0.5
2. Medium size effect: 0.5 ≤ Cohen’s d < 0.8
3. Large effect size: Cohen’s d > 0.8

Note: These thresholds are general guidelines, and the interpretation may depend on the specific context of your study.

Step by Step Procedure to calculate Cohen’s d in R

Method 1: Calculate Cohen’s d in R using lsr

Step 1: Package Installation

install.packages("lsr")
library(lsr)

Step 2: Creating Data Set

group1 <- c(21, 20, 18, 16, 12, 14, 15, 16, 11, 11, 9, 8)
group2 <- c(23, 20, 16, 10, 11, 11, 12, 14, 14, 10, 9, 7)

Step 3: Calculate Cohen’s d

cohensD(group1, group2)

R

#Step 1: Package Installation install.packages("lsr") library(lsr) #Step 2: Creating Data Set group1 <- c(21, 20, 18, 16, 12, 14, 15, 16, 11, 11, 9, 8) group2 <- c(23, 20, 16, 10, 11, 11, 12, 14, 14, 10, 9, 7) #Step 3: Calculate Cohen's d cohensD(group1, group2)

Output:

0.2635333

Using the rule of thumb mentioned earlier, we would interpret this to be a small effect size.

Method 2: Calculate Cohen’s d in R using effsize

Step 1: Package Installation

install.packages("effsize")
library(effsize)

Step 2: Creating Data Set

group1 <- c(21, 20, 18, 16, 12, 14, 15, 16, 11, 11, 9, 8)
group2 <- c(23, 20, 16, 10, 11, 11, 12, 14, 14, 10, 9, 7)

Step 3: Calculate Cohen’s d

cohen.d(group1, group2)

R

#Step 1: Package Installation install.packages("effsize") library(effsize) #Step 2: Creating Data Set group1 <- c(21, 20, 18, 16, 12, 14, 15, 16, 11, 11, 9, 8) group2 <- c(23, 20, 16, 10, 11, 11, 12, 14, 14, 10, 9, 7) #Step 3: Calculate Cohen's d cohen.d(group1, group2)

Output:

d estimate: 0.2635333 (small)
95 percent confidence interval:
lower upper
-0.5867889 1.1138555

Using the rule of thumb mentioned earlier, we would interpret this to be a small effect size.

Conclusion

In this article, we learnt about How to Calculate Cohen’s d in R. Cohen’s d is a measure that indicates the difference between two means. It is commonly used to quantify the magnitude of the difference between two groups in a study. We learnt about 2 different libraries using effsize and Isr