Point biserial correlation coefficient and its generalization

The problem of measuring the association between two characters, one quantitative and the other qualitative, is discussed. The formula for the large sample standard error of the point biserial correlation coefficient under general conditions is derived. The point multiserial correlation coefficient is introduced and some of its properties are examined. Tests of different hypotheses appropriate to these types of problems are formulated.I wish to pay my sincerest thanks to Dr. C. R. Rao, Dr. S. K. Mitra, and the reviewers for their valuable suggestions.