The relation of multiserial eta to other measures of correlation

Ordinary product-moment correlation and regression methods are frequently not immediately applicable to qualitative data, whereas multiserialr, point-multiserialr, and multiserial eta can be easily applied. The multiserialr is rejected for prediction since it tells us only what the correlationmight be if certain assumptionswere true and if wecould measure what isnot now measured. The point-multiserialr and multiserial eta are identical when the number of categories is two but differ when it is three or greater. The multiserial eta is identical with the product-momentr when categories are assigned scale values equal to their means on the continuous variable. With three or more categories, the point-multiserialr, whichassumes linearity withequal step intervals, is always lower than the multiserial eta, whichforces linearity by adoption ofunequal step intervals based upon difference in criterion attainment. While the multiserial eta expends one degree of freedom with the weighting of each category, this is known and correctable, whereas the vague partial loss of degrees of freedom due to the ordering of categories in the point-multiserial is not correctable.Personnel Research Section, A.G.O.