Published online by Cambridge University Press: 01 August 2014
A generalization of the F test is proposed to see how many independent components are statistically significant when the co-variances between DZ twin differences on several psychological tests are compared with similar co-variances for MZ twins. When applied to the 6 scores of Thurstone's Primary Mental Abilities test battery, at least 4 separate components were found to be significant independently. Then 4 components are tentatively identified as similar to, although not identical with, the Number, Verbal, Space and Word fluency scores. While the procedure bears some resemblance to factor analysis, it may lead to quite different results since it is based on the comparison of two co-variance matrices of twin differences.
In conclusion, it should be kept in mind that these results are based on small samples of MZ and DZ twins, so that a repetition of the study seems indicated. This replication is now in progress.
Acknowledgments. This report is based on data obtained in the Hereditary Abilities Study of the Institute of Human Biology of the University of Michigan of which Lee R. Dice was the principal investigator. The study was supported by McGregor Fund of Detroit and by grant M-1045 of the National Institute of Mental Health. The help of Mrs. Kathryn Goode and of the staff of the University of Michigan Computing Laboratory is gratefully acknowledged in obtaining the covariance matrices. For the solution of the characteristic equations I am indebted to Charles Wrigley and Peter Hemingway of Michigan State University and to MISTIC. Support while writing the paper was received from NIH grants RG-5527, M-6203 and MH-07033-01 and National Science Foundation grant GB-466.
While I am solely responsible for the ideas in this paper, I have profited from correspondence or discussions with Drs. Batschelet, Dempster, Dwyer, Hotelling, Lawley, Lubin, Tucker, Tukey and others.