On the relation between the phi-coefficient and the tetrachoric correlation coefficient
(English)Manuscript (Other academic)
We show existence of a continuous bijection between the tetrachoric correlation coefficient and the phi-coefficient under given marginal probabilities. Implications are that the tetrachoric correlation coefficient can be calculated using the assumptions of the phi-coefficient construction, and the phi-coefficient can be calculated using the assumptions of the tetrachoric correlation construction. As a consequence, whether to use the phi-coefficient or the tetrachoric correlation coefficient is a matter of preference only. The result can also be used to construct a numerical table of tetrachoric correlation coefficients, converted from the marginal probabilities and the phi-coefficient, which is easy to calculate by hand. Moreover, a mathematically rigorous definition of the tetrachoric correlation coefficient is provided, along with a proof that the coefficient is well defined.
phi-coefficient, tetrachoric correlation coefficient, 2 x 2 contingency table, measure of association, dichotomous variables
Probability Theory and Statistics
Research subject Statistics
IdentifiersURN: urn:nbn:se:uu:diva-100692OAI: oai:DiVA.org:uu-100692DiVA: diva2:210881