Olkin's New Formula for Significance of r13 vs. r23 Compared with Hotelling's Method.

The article presents information about two alternate formulas for determining the significance of the difference between a certain two correlation coefficients. These coefficients, r13 and r23, denote the correlation of two predictor variables with a predictand within a single sample drawn from a population. A restrictive assumption made in the derivation of statistician Harold Hotelling's formula is that the sets of values associated with the predictor variables must be fixed for all possible samples. In contrast, the restrictive assumption underlying the formula derived by statistician Ingram Olkin is that the three variables have a trivariate normal distribution. However, the sets of values associated with each variable are not fixed. Thus, the results obtained by this procedure can be generalized from the sample to the population from which it was drawn.