The phi coefficient is the Pearson correlation coefficient for two binary variables. For a 
contingency table
with cell counts
 |
(1)
|
it is
 |
(2)
|
Its magnitude is between 0 and 1 when all marginal totals are positive. For a 
table, its absolute value equals
Cramer's V.
See also
Contingency Table,
Correlation
Coefficient,
Cramer's V
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References
Edwards, A. L. "The Phi Coefficient." §7.2 in An
Introduction to Linear Regression and Correlation. San Francisco, CA: W. H. Freeman,
pp. 68-72, 1976.
Cite this as:
Weisstein, Eric W. "Phi Coefficient."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PhiCoefficient.html
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