Phi/Phimax: Review and Synthesis

Abstract

This paper explores the phimax adjustment to phi. It shows phi/phimax to be a measure of relationship apart from its affiliation with phi. The adjustment when the variables are inversely related, phimin, is also considered. Next is a discussion of the relation between phi/phimax and kappa. The article ends with an analytical look at phi/phimax. Some findings of this exploration are: phi/phimax is an asymmetrical, equal-interval step function with ties to probability. Finally, phi/phimax is shown to be nonrobust in situations where it should be most useful.

Researcher Bias: The Use of Machine Learning in Software Defect Prediction

“…One slightly awkward property of the φ coefficient, and therefore MCC, is that depending upon the marginal distributions of the confusion matrix, plus or minus unity may not be attainable and so some statisticians propose a φ/φ max rescaling [32]. We choose not to follow this procedure since it results in an over-sensitive measures of association in that a very small change in the count of correctly classified instances (TP or TN) lead to unintuitively large changes in the correlation.…”

“…First, our observations are assuredly not a random sample since researchers tend to report their 'best' or most 'interesting' results. Second, depending upon the marginal probabilities of the confusion matrix MCC is constrained to values less than unity (minus unity) [32] What is striking, however, is the number of observations of the correlation coefficient being close to zero or even negative. This reveals that many classifiers are performing extremely poorly, since zero indicates no relationship at all and could therefore be achieved through guessing.…”

On Association Coefficients, Correction for Chance, and Correction for Maximum Value

“…In the literature, it has been suggested to replace the phi coefficient by the ratio phi/phimax, where phimax is the maximum value of the phi coefficient given the marginal probabilities. A detailed review of the phi/phimax literature is presented in Davenport and El-Sanhurry (1991).…”

A New Physarum Learner for Network Structure Learning from Biomedical Data

“…As the main goal of this study is to examine whether it is generally possible to learn Bayesian Network structure with the Physarum Solver, for the sake of simplicity we restricted the benchmark data sets to be binary. This restriction allows to use the simple normalized correlation coefficient φ given by (Davenport and El-Sanhurry, 1991) …”