The Phi-coefficient, the Tetrachoric Correlation Coefficient, and the Pearson-Yule Debate

摘要: Author(s): Ekstrom, Joakim | Abstract: Two measures of association for dichotomous variables, the phi-coefficient and tetrachoric correlation coefficient, are reviewed differences between two discussed in context famous so-called Pearson-Yule debate, that took place early 20th century. The given mathematically rigorous definitions, their underlying assumptions formalized, some key properties derived. Furthermore, existence a continuous bijection coefficient under marginal probabilities is shown. As consequence, can be computed using construction, construction. efforts lead to an attempt reconcile showing fact more similar than different two, choice measure does not carry substantial impact on conclusions analysis.