Selecting the right correlation measure for binary data

Finding the most interesting correlations among items is essential for problems in many commercial, medical, and scientific domains. Although there are numerous measures available for evaluating correlations, different correlation measures provide drastically different results. Piatetsky-Shapiro provided three mandatory properties for any reasonable correlation measure, and Tan et al. proposed several properties to categorize correlation measures; however, it is still hard for users to choose the desirable correlation measures according to their needs. In order to solve this problem, we explore the effectiveness problem in three ways. First, we propose two desirable properties and two optional properties for correlation measure selection and study the property satisfaction for different correlation measures. Second, we study different techniques to adjust correlation measures and propose two new correlation measures: the Simplified x² with Continuity Correction and the Simplified x² with Support. Third, we analyze the upper and lower bounds of different measures and categorize them by the bound differences. Combining these three directions, we provide guidelines for users to choose the proper measure according to their needs.