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# Phi coefficient

The 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, r1 r2 are their row totals, and c1 c2 are their column totals:
 y=0 y=1 x=0 a b r1 x=1 c d r2 c1 c2 n

Given which the phi coefficient is (ad-bc)/√(r1r2c1c2)

Note that the phi coefficient, unlike Pearson's correlation coefficient, cannot be assumed to lie in the range -1 to +1. Except where otherwise specified, all text and images on this page are copyright InfluentialPoints, all rights reserved. Images not copyright InfluentialPoints credit their source on web-pages attached via hypertext links from those images.