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 mu ltiple correlation coefficients for 2 independent samples. In 1 method, the researcher constructs a confidence interval for the difference between 2 p opulation squared coefficients; in the 2nd method, a Fisher-type transforma tion of the sample squared correlation coefficient is used to obtain a test statistic. Both methods are based on asymptotic theory and use approximati ons to the sampling variance. The approximations are incorrect when the pop ulation multiple correlation coefficient is zero. The 2 procedures were exa mined for equal and unequal population multiple correlation coefficients in combination with equal and unequal sample sizes. As expected, the procedur es were inaccurate when the population multiple correlation coefficients we re zero or very small and, in some conditions, were inaccurate when sample sizes and coefficients were unequal.