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Introduced by Karl Pearson this measure is similar to the Pearson correlation the binary correlation coefficient example in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. Two binary variables are considered positively associated if most of the data falls along the diagonal cells.
In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. The phi coefficient that describes the association of x and y is. The phi coefficient has a maximum value that is determined by the distribution of the two variables if one or both variables can take on more than two the binary correlation coefficient example. See Davenport El-Sanhury  for a thorough discussion. From Wikipedia, the free encyclopedia.
Mathematical Methods of Statistics. Princeton University Press, p. Equating r-based and d-based effect-size indices: Problems with a commonly recommended formula. The binary correlation coefficient example and Psychological Measurement, 51, — Mean arithmetic geometric harmonic Median Mode.
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