*56*

**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 = √(X ^{2}/n) / min(c-1, r-1)**

where:

**X**The Chi-square statistic^{2}:**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