Product correlation was studied under the condition that the original variables are jointly distributed multivariate normal with equal coefficients of variation. Dependent upon the value of the common coefficient of variation, product correlation was shown to be a quantity ranging between two extremes: (a) sum correlation; and (b) either the value zero or an unfamiliar function of the intercorrelations among the original variables. Product correlations calculated by systematically varying the common coefficient of variation and the common intercorrelation among all original variables revealed the similarity between product correlation and sum correlation for many data applications.
Get full access to this article
View all access options for this article.
References
1.
Glass, G. V.Correlations with products of variables: Statistical formulation and implications for methodology. American Educational Research Journal, 1968, 5, 721-728.
2.
Graybill, F. A.An introduction to linear statistical models. Vol.1. New York: McGraw-Hill, 1961.
3.
Isserlis, L.On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables. Biometrika, 1918, 12, 134-139.
4.
Kowalski, C. J.On the effects of non-normality on the distribution of the sample product-moment correlation coefficient . Applied Statistics, 1972, 21, 1-12.
5.
Moss, J., Jr. and Duenk, L. G.Estimating the concurrent validity of the Minnesota Tests of Creative Thinking. American Educational Research Journal, 1967, 4, 387-396.
6.
Sockloff, A. L.Product variables and product correlation: Some results. Technical Report 74-3. Philadelphia : Measurement and Research Center, Temple University , 1974.
7.
Sockloff, A. L.Spurious product correlation . EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1976, 36, 33-44.
8.
Spearman, C.Correlations of sums and differences . British Journal of Psychology, 1913 , 5, 417-426.
9.
Wishart, J. and Bartlett, M. S.The distribution of second order moment statistics in a normal system. Proceedings of the Cambridge Philosophical Society, 1932, 28, 455-459.
