The Reliability of a Point Biserial Coefficient of Correlation

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Abstract
An attempt is made to elaborate upon Lev's results concerning the reliability of the point biserial coefficient of correlation in a manner that will be helpful to the psychological statistician. Procedures required in the use of the non-central t tables prepared by Johnson and Welch are described as they relate to the determination of the fiducial limits for a point biserial coefficient. A normal approximation technique for the estimation of fiducial limits is also suggested. Numerical evidence is presented which shows that relative to a given level of significance the width of the fiducial interval estimated from a point biserial coefficient of any size is smaller than that of the fiducial interval corresponding to an ordinary Pearsonian coefficient of the same magnitude.

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