Compute Cramer's V

cramer_v() computes Cramer's V for a two-way frequency table, measuring the strength of association between two categorical variables.

Usage

cramer_v(x)

Arguments

x

A contingency table (of class table) for which to compute the statistic.

Value

A numeric vector of length 1, representing the Cramer's V statistic.

Details

Cramer's V is computed as \(V = \sqrt{\chi^2 / (n \cdot (k - 1))}\), where \(\chi^2\) is the Pearson chi-squared statistic, \(n\) is the total number of observations, and \(k = \min(r, c)\) with \(r\) and \(c\) the number of rows and columns. It is suitable for nominal (unordered categorical) variables.

Examples

# Example with mtcars dataset
data(mtcars)

# Discretize continuous variables
mtcars$gear <- as.factor(mtcars$gear)
mtcars$cyl <- as.factor(mtcars$cyl)

# Create contingency table
tab <- table(mtcars$gear, mtcars$cyl)

# Compute Cramer's V
cramer_v(tab)
#> Warning: Chi-squared approximation may be incorrect
#> [1] 0.5308655