| Abstract: | The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to carry out one-sided tests (null hypothesis may involve a nonzero value for the multiple correlation coefficient) to attain a specified power is given. Sample size calculation for computing confidence intervals for the squared multiple correlation coefficient with a specified expected width is also provided. Sample sizes for powers and confidence intervals are tabulated for a wide range of parameter configurations and dimensions. The results are illustrated using the empirical data from Timm (1975) Timm, N. H. 1975. Multivariate analysis with applications in education and psychology, Belmont, CA: Wadsworth. [Google Scholar] that related scores from the Peabody Picture Vocabulary Test to four proficiency measures. |
