What is the Phi Coefficient?

The Phi Coefficient is a measure up of association in between two binary variables (i.e. Living/dead, black/white, success/failure). The is also called the Yule phi or median Square Contingency Coefficient and is offered for contingency tables when:




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Solution: Insert the counts into the formula and also solve.Φ = ad – bc / √((a + b)(c + d)(a + c)(b + d))Φ = 14*13 – 10*6 / √((14 + 10)(6 + 13)(14 + 6)(10 + 13))Φ = 182 – 60 / √((24)(19)(20)(23))Φ = 122/ √((24)(19)(20)(23))Φ = 122/ 458Φ = 0.266.

Interpreting the Phi Coefficient

The phi coefficient is a symmetrical statistic, which way the live independence variable and dependent variables room interchangeable.The translate for the phi coefficient is comparable to the Pearson Correlation Coefficient. The range is native -1 come 1, where:

0 is no relationship.1 is a perfect confident relationship: most of your data drops along the diagonal cells. -1 is a perfect an adverse relationship: many of her data is not on the diagonal.

The Political science Department in ~ Quinnipiac university posted this beneficial list that the an interpretation of Pearson’s Correlation coefficients. The same dominance of thumb can be offered for the Phi coefficient. Note that these room “crude estimates” for interpreting strengths of relationships.

r value =
+.70 or higherVery solid positive relationship
+.40 come +.69Strong hopeful relationship
+.30 come +.39Moderate confident relationship
+.20 to +.29weak hopeful relationship
+.01 come +.19No or negligible connection
0No partnership
-.01 come -.19No or negligible relationship
-.20 to -.29weak an adverse relationship
-.30 come -.39Moderate an unfavorable relationship
-.40 come -.69Strong an adverse relationship
-.70 or higherVery strong an unfavorable relationship

References:Quinnipiac University. Maaning the Pearson’s. Recall Jun 20, 2016 from: http://faculty.quinnipiac.edu/libarts/polsci/Statistics.htmlYule, G. U. (1912). J. R. Statist. Soc., 75,576–642. (On the approaches of measuring theassociation in between two variables. The firstidentification of the phi-coefficient.)


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