Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Ronald V. Canfield


The logical steps performed when doing a factor analysis can be classified into three operation s. The first step concerns the exact mode of analysis and involves the type of centering, scaling and formation o f sums of squares . The second step involves extraction of initial factors. The algebraic basis of the factors are rotated in the last step to obtain a more easily interpreted set of factors. At each step several different methods have been suggested and appear in the literature. Two primary modes of factor analysis are commonly used an d they are denoted as R-mode and Q-mode.

This study reviews different modes of facto r analysis, i.e., R-Q, P-0, and T-S, and investigate the relationship between Rand Q mode in terms of the number and the interpretation of factors. It has been demenstrated that in principal component analysis, the factors of Rand Q mode are trans positions of each other, i.e., the factors of the one kind of analysis a re identical with the loadings of the other. In this study, it has been found that the number of significant factors is different for the two modes of analysis although the ranks of their correlation matrix are the same. In terms of interpretations, the two modes come up with the same basic dimensions and concepts although they are not one-one corresponding. Finally, an example is given to illustrate the points found in this study.