How to Interpret Cramer’s V (With Examples)


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 perfect 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

How to Interpret Cramer’s V

The following table shows how to interpret Cramer’s V based on the degrees of freedom:

Degrees of freedom Small Medium Large
1 0.10 0.30 0.50
2 0.07 0.21 0.35
3 0.06 0.17 0.29
4 0.05 0.15 0.25
5 0.04 0.13 0.22

The following examples show how to interpret Cramer’s V in different situations.

Example 1: Interpreting Cramer’s V for 2×3 Table

Suppose we want to know if there is an association between eye color and gender so we survey 50 individuals and obtain the following results:

We can use the following code in R to calculate Cramer’s V for these two variables:

library(rcompanion)

#create table
data = matrix(c(6, 9, 8, 5, 12, 10), nrow=2)

#view table
data

     [,1] [,2] [,3]
[1,]    6    8   12
[2,]    9    5   10

#calculate Cramer's V
cramerV(data)

Cramer V 
  0.1671

Cramer’s V turns out to be 0.1671.

The degrees of freedom would be calculated as:

  • df = min(#rows-1, #columns-1)
  • df = min(1, 2)
  • df = 1

Referring to the table above, we can see that a Cramer’s V of 0.1671 and degrees of freedom = 1 indicates a small (or “weak”) association between eye color and gender.

Example 2: Interpreting Cramer’s V for 3×3 Table

Suppose we want to know if there is an association between eye color and political party preference so we survey 50 individuals and obtain the following results:

We can use the following code in R to calculate Cramer’s V for these two variables:

library(rcompanion)

#create table
data = matrix(c(8, 2, 4, 5, 8, 6, 6, 3, 8), nrow=3)

#view table
data

     [,1] [,2] [,3]
[1,]    8    5    6
[2,]    2    8    3
[3,]    4    6    8

#calculate Cramer's V
cramerV(data)

Cramer V 
  0.246

Cramer’s V turns out to be 0.246.

The degrees of freedom would be calculated as:

  • df = min(#rows-1, #columns-1)
  • df = min(2, 2)
  • df = 2

Referring to the table above, we can see that a Cramer’s V of 0.246 and degrees of freedom = 2 indicates a medium (or “moderate”) association between eye color and political party preference.

Additional Resources

The following tutorials explain how to calculate Cramer’s V in different statistical software:

How to Calculate Cramer’s V in Excel
How to Calculate Cramer’s V in R
How to Calculate Cramer’s V in Python

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