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Phi coefficientThe phi coefficient, a measure of association between two binary variables (x & y), is sometimes described as a special case of Pearson's correlation coefficient. Two binary are positively associated if most of the data fall along the leading diagonal (\) cells (a&d), and negatively correlated when the converse is true (/) cells b & c, below. In the following table, a, b, c, d, denote the cell frequencies, r_{1} r_{2} are their row totals, and c_{1} c_{2} are their column totals:
Given which the phi coefficient is (adbc)/√(r_{1}r_{2}c_{1}c_{2}) Note that the phi coefficient, unlike Pearson's correlation coefficient, cannot be assumed to lie in the range
