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This study compares eleven tests of the null hypothesis Ho: P12 = P13 where pij is the population correlation coefficient between the ith variable Xi and the jth variable Xi; X1 is the dependent variable and X2 and X3 are the independent variables, and where the data consists of a sample from a trivariate normal distribution. The methods include the likelihood ratio test, Aitken's test, Hotelling's test, and Williams' test. Asymptotic comparisons of level of significance are made; small sample simulation results are given on level of significance and power. For small or moderate samples, Williams' statistic emerges as the best choice; for very large samples, the likelihood ratio test wouild be preferred except for computational difficulties.
Neill et al. (Sun,) studied this question.