Which measure describes the strength of association between two categorical variables with more than two categories, as a variant of phi?

Which measure describes the strength of association between two categorical variables with more than two categories, as a variant of phi?

• A. Phi coefficient
• B. Kappa statistic
• C. Contingency coefficient
• D. Cramér's V

Answer: (D)

When comparing two categorical variables with more than two categories, you want a measure that stays on a 0 to 1 scale and reflects how strongly the variables are related, not just whether they’re independent. Cramér’s V provides that by building on the chi-square statistic and adjusting for the size of the table, giving a consistent strength measure across different numbers of categories. It ranges from 0 (no association) to 1 (perfect association) and, in the 2x2 case, it reduces to the phi coefficient, which is why it’s considered the natural generalization of phi for larger tables. The formula is V = sqrt( χ² / (n × min(r−1, c−1)) ), where χ² is Pearson’s chi-square, n is the total sample size, and r and c are the numbers of rows and columns. Other options either target agreement rather than association, are restricted to 2x2 tables, or have less interpretable upper bounds across different table sizes, making Cramér’s V the best choice here.

When comparing two categorical variables with more than two categories, you want a measure that stays on a 0 to 1 scale and reflects how strongly the variables are related, not just whether they’re independent. Cramér’s V provides that by building on the chi-square statistic and adjusting for the size of the table, giving a consistent strength measure across different numbers of categories. It ranges from 0 (no association) to 1 (perfect association) and, in the 2x2 case, it reduces to the phi coefficient, which is why it’s considered the natural generalization of phi for larger tables. The formula is V = sqrt( χ² / (n × min(r−1, c−1)) ), where χ² is Pearson’s chi-square, n is the total sample size, and r and c are the numbers of rows and columns. Other options either target agreement rather than association, are restricted to 2x2 tables, or have less interpretable upper bounds across different table sizes, making Cramér’s V the best choice here.