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The phi coefficient (represented symbolically as φ) is a test of the relationship or association between two dichotomous variables. In other words, both variables have only two, mutually exclusive responses options, such as yes/no or left-handed/right-handed. The phi coefficient ranges from −1 to +1, with negative numbers representing negative relationships, zero representing no relationship, and positive numbers representing positive relationships. This entry discusses the setup, calculation, and interpretation of a phi coefficient. It concludes by presenting a brief example using communication variables.

Setup and Calculation of a Phi Coefficient

To compute a phi coefficient, two variables must be used, each with dichotomous response options. This produces what is called a 2 × 2 (two variables, each with two response options) contingency table, which displays the variables, their ...

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