Comparing squared multiple correlation coefficients. Examination of a confidence interval and a test of significance

I. Olkin and J. D. Finn (1995) presented 2 methods for comparing squared multiple correlation coefficients for 2 independent samples. In 1 method, the researcher constructs a confidence interval for the difference between 2 population squared coefficients; in the 2nd method, a Fisher-type transformation of the sample squared correlation coefficient is used to obtain a test statistic. Both methods are based on asymptotic theory and use approximations to the sampling variance. The approximations are incorrect when the population multiple correlation coefficient is zero. The 2 procedures were examined for equal and unequal population multiple correlation coefficients in combination with equal and unequal sample sizes. As expected, the procedures were inaccurate when the population multiple correlation coefficients were zero or very small and, in some conditions, were inaccurate when sample sizes and coefficients were unequal.