How to Calculate Cramer’s V in R

Cramer’s V is a measure of the strength of association between two nominal variables.

It ranges from 0 to 1 where:

• 0 indicates no association between the two variables.
• 1 indicates a strong association between the two variables.

It is calculated as:

Cramer’s V = √(X²/n) / min(c-1, r-1)

where:

• X²: The Chi-square statistic
• n: Total sample size
• r: Number of rows
• c: Number of columns

This tutorial provides a couple examples of how to calculate Cramer’s V for a contingency table in R.

Example 1: Cramer’s V for a 2×2 Table

The following code shows how to use the CramerV function from the rcompanion package to calculate Cramer’s V for a 2×2 table:

#create 2x2 table
data = matrix(c(7,9,12,8), nrow = 2)

#view dataset
data

     [,1] [,2]
[1,]    7   12
[2,]    9    8

#load rcompanion library
library(rcompanion)

#calculate Cramer's V
cramerV(data)

Cramer V 
  0.1617

Cramer’s V turns out to be 0.1617, which indicates a fairly weak association between the two variables in the table.

Note that we can also produce a confidence interval for Cramer’s V by indicating ci = TRUE:

cramerV(data, ci = TRUE)

  Cramer.V lower.ci upper.ci
1   0.1617 0.003487   0.4914

We can see that Cramer’s V remains unchanged at 0.1617, but we now have a 95% confidence interval that contains a range of values that is likely to contain the true value of Cramer’s V.

This interval turns out to be: [.003487, .4914].

Example 2: Cramer’s V for Larger Tables

Note that we can use the CramerV function to calculate Cramer’s V for a table of any size.

The following code shows how to calculate Cramer’s V for a table with 2 rows and 3 columns:

#create 2x3 table
data = matrix(c(6, 9, 8, 5, 12, 9), nrow = 2)

#view dataset
data

     [,1] [,2] [,3]
[1,]    6    8   12
[2,]    9    5    9

#load rcompanion library
library(rcompanion)

#calculate Cramer's V
cramerV(data)

Cramer V 
  0.1775

Cramer’s V turns out to be 0.1775.

You can find the complete documentation for the CramerV function here.

Additional Resources

Chi-Square Test of Independence in R
Chi-Square Goodness of Fit Test in R
Fisher’s Exact Test in R