CORRELATION ANALYSIS FOR SIMULTANEOUSLY CONTROLLING RELIABILITY AND VALIDITY

Abstract

The purpose of the present study is to propose a procedure for correlation analysis of several (especially two) sets of variables, which includes canonical correlation analysis, principal component analysis, and multiple regression analysis as a special case. The proposed method derives components from each set of variables which maximize the weighted geometric mean of two types of indicators: one is the contribution rate of the components for their original variables, the other is the squared correlation between the components. In terms of the test theory, the former are indicators of reliability and the latter are indicators of concurrent validity. Through the numerical examples applying this method to the data of two Japanese language personality inventory, the method is shown to be particularly useful when determining the weights for test items.