The paper by E. L. Lehmann explores the concept of dependence in pairs of variables $(X, Y)$, focusing on bivariate normal distributions and $2 \times 2$ tables. The main problems studied are tests of independence and the definition and estimation of measures of association. Lehmann introduces three definitions of positive dependence: quadrant dependence, regression dependence, and likelihood ratio dependence. Each definition is investigated through examples and their implications are explored. The paper also discusses the statistical applications of these concepts, particularly in the context of testing hypotheses and controlling error rates in multiple decision procedures. Key results include the unbiasedness of certain tests of independence and the conditions under which these tests are valid. The paper provides a comprehensive framework for understanding and applying these concepts in statistical analysis.The paper by E. L. Lehmann explores the concept of dependence in pairs of variables $(X, Y)$, focusing on bivariate normal distributions and $2 \times 2$ tables. The main problems studied are tests of independence and the definition and estimation of measures of association. Lehmann introduces three definitions of positive dependence: quadrant dependence, regression dependence, and likelihood ratio dependence. Each definition is investigated through examples and their implications are explored. The paper also discusses the statistical applications of these concepts, particularly in the context of testing hypotheses and controlling error rates in multiple decision procedures. Key results include the unbiasedness of certain tests of independence and the conditions under which these tests are valid. The paper provides a comprehensive framework for understanding and applying these concepts in statistical analysis.