Testing Independence with Contingency Tables | CFA Level I Quantitative Methods

In this lesson, we’ll explore the test of independence using contingency tables. This non-parametric test is ideal for examining the relationship between two categorical or discrete variables.

Contingency Tables: A Quick Overview

In our previous lessons, we covered the parametric approach and the Spearman Rank correlation approach for testing correlation between two random variables. However, these methods aren’t suitable for categorical or discrete data. That’s where contingency tables come in handy!

For example, suppose we want to investigate if a firm’s size is independent of the stock classification (growth, value, or blend). We’d use a contingency table to analyze the relationship between these categorical variables.

Performing a Test of Independence Using a Contingency Table

Follow these steps to perform a test of independence with a contingency table:

1. Calculate the total observations for each category.
2. Compute the expected frequencies for each cell.
3. Calculate the degrees of freedom. df = (r-1)(c-1)
4. Obtain the critical value from the Chi-square table based on the degrees of freedom and the level of significance.
5. Define the decision rule using the critical value.
6. Calculate the contributions to the test statistic for each cell, and sum them up.
7. Check the test statistic against the decision rule.

Conclusion

And that’s a wrap! You’ve learned how to perform a test of independence using contingency tables, suitable for categorical or discrete variables.