Statistical measure of association for two binary variables
In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a measure of association for two binary variables.
In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975.[1]
Introduced by Karl Pearson,[2] and also known as the Yule phi coefficient from its introduction by Udny Yule in 1912[3] this measure is similar to the Pearson correlation coefficient in its interpretation.
^Matthews, B. W. (1975). "Comparison of the predicted and observed secondary structure of T4 phage lysozyme". Biochimica et Biophysica Acta (BBA) - Protein Structure. 405 (2): 442–451. doi:10.1016/0005-2795(75)90109-9. PMID 1180967.
^Cramer, H. (1946). Mathematical Methods of Statistics. Princeton: Princeton University Press, p. 282 (second paragraph). ISBN 0-691-08004-6 https://archive.org/details/in.ernet.dli.2015.223699
^Yule, G. Udny (1912). "On the Methods of Measuring Association Between Two Attributes". Journal of the Royal Statistical Society. 75 (6): 579–652. doi:10.2307/2340126. JSTOR 2340126.
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