How to Calculate Cramer’s V in R

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Understanding the association between categorical variables is vital in data analysis. In this article, we’ll utilize the mtcars dataset to calculate Cramer’s V in R, providing insights into the relationship between a car’s gearbox type and its number of cylinders.

1. Dataset Overview

The mtcars dataset in R comprises various car specifications. For our analysis, we’re interested in:

  • am: Gearbox type (0 = automatic, 1 = manual)
  • cyl: Number of cylinders (4, 6, or 8)

2. Assumptions and Data Types

Ensure that the data used for Cramer’s V is categorical. Both am and cyl in the mtcars dataset are categorical, making them apt for our analysis.

3. Calculating Cramer’s V with mtcars

Here’s the guide to compute Cramer’s V using the mtcars dataset:

# Load the dataset

# Perform the Chi-Square Test
chi_sq_test <- chisq.test(mtcars$am, mtcars$cyl)

# Calculate Cramer’s V
n <- sum(chi_sq_test$observed)  
k <- min(nrow(chi_sq_test$observed) - 1, ncol(chi_sq_test$observed) - 1)  

cramers_v <- sqrt(chi_sq_test$statistic / (n * k))

4. Interpreting the Results

After executing the above R code, you’ll get a Cramer’s V value. Use the following scale:

  • Near 0: Weak association
  • Near 1: Strong association

Typical thresholds:

  • 0.1: Small association
  • 0.3: Medium association
  • 0.5 or higher: Strong association

5. Visualization of Associations

Visualizing can help in better understanding:

mosaicplot(table(mtcars$am, mtcars$cyl), main="Mosaic plot of Gearbox type vs Number of Cylinders")

6. Potential Caveats

  1. Symmetry: Cramer’s V doesn’t specify the direction of association.
  2. No Causality: A significant association doesn’t infer a cause-and-effect relationship.

7. Conclusion

The mtcars dataset offers a practical application of Cramer’s V in R. Understanding associations between categorical variables, like the gearbox type and the number of cylinders in a car, provides meaningful insights and informs data-driven decisions.

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