A likelihood ratio test for the equality of two partial correlation coefficients based on two independent multinormal samples has been derived. The large sample Z-test for the same problem has also been discussed. The power analysis of the two tests is obtained. It has been found that the approximate likelihood ratio (ALR) test showed consistently better results than Z -test in terms of power. The size of the ALR test is slightly more than the alpha level. The ALR test is recommended strongly for use in practice.
Bhandary, Madhusudan and Gupta, Arjun K.
"Test for the Equality of Partial Correlation Coefficients for Two Populations,"
Journal of Modern Applied Statistical Methods: Vol. 14
, Article 10.
Available at: http://digitalcommons.wayne.edu/jmasm/vol14/iss1/10