Standard Article

Phi Coefficient

  1. Stanley Wearden

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0677

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Wearden, S. 2010. Phi Coefficient. Corsini Encyclopedia of Psychology. 1.

Author Information

  1. West Virginia University

Publication History

  1. Published Online: 30 JAN 2010


The phi (φ) coefficient was proposed by George Utney Yule in 1912 as an index of association between two dichotomous variables. The φ statistic is particularly useful to many research workers because it is the familiar product-moment correlation when computed for data from a bivariate binomial distribution. When such data are organized in a fourfold table, the coefficient is most easily computed as

  • mathml alt image


  • statistics;
  • two sample comparisons;
  • correlation