*50*

**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 = √(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

**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