Which scenario is the Phi-coefficient appropriate for?

Which scenario is the Phi-coefficient appropriate for?

• A. One variable is dichotomous and the other is continuous
• B. Both variables are dichotomous
• C. Both variables are continuous
• D. One variable is ordinal and the other is nominal

Answer: (B)

The Phi coefficient is used to measure the association between two binary (dichotomous) variables. It’s the Pearson correlation applied to data coded as 0/1, so it fits perfectly when both variables have only two categories. In a 2x2 contingency table, Phi tells you whether having one category of one variable tends to occur with a particular category of the other more or less than would be expected by chance. The value ranges from -1 to 1, with the magnitude indicating the strength of the association and the sign indicating the direction, depending on how you code the binary categories. This measure isn’t appropriate when one or both variables are not binary (for example, continuous or multi-category nominal variables), in which case other statistics are used (such as point-biserial for a binary and a continuous variable, or Cramér’s V for nominal data with more than two categories).

The Phi coefficient is used to measure the association between two binary (dichotomous) variables. It’s the Pearson correlation applied to data coded as 0/1, so it fits perfectly when both variables have only two categories. In a 2x2 contingency table, Phi tells you whether having one category of one variable tends to occur with a particular category of the other more or less than would be expected by chance. The value ranges from -1 to 1, with the magnitude indicating the strength of the association and the sign indicating the direction, depending on how you code the binary categories. This measure isn’t appropriate when one or both variables are not binary (for example, continuous or multi-category nominal variables), in which case other statistics are used (such as point-biserial for a binary and a continuous variable, or Cramér’s V for nominal data with more than two categories).