A comparison of rotated structures of principal components extracted from two types of correlation matrices

The purpose of this study was to compare the results of principal component extraction from a parametric correlation matrix (Pearson Product-Moment correlation) with the factors extracted from a nonparametric correlation matrix (Spearman Rank correlation). The scope of the study included an empirical comparison of the component structures with respect to the number of variables significantly associated with each factor as well as the number of significant factors in the data sets. A secondary purpose of the study was to validate the application of principal components analysis employing nonparametric matrices for the extraction of components to biomedical and public health data.;In evaluating factor significance, two criteria were used in tandem, the Kaiser-Guttman (KG) root of unity test and Cattell's scree test. Variable loadings were considered significant if the absolute value of the loading was greater than or equal to the standard error of the loading. The rotated component structures were evaluated for similarity using coefficients of concordance. Analogous components were determined to be statistically similar if the coefficient of concordance was greater than or equal to the critical value of the Pearson Product-Moment correlation coefficient.;Results indicate that when nominal variables are present in the data set, while the results are not statistically different, the empirical interpretations from the two different component structures are different. Therefore, when variables lacking a normal distribution are included in a data set, extraction from an appropriate nonparametric matrix, such as a Spearman Rho correlation matrix, is warranted. When the variables of interest are ordinal, interval and/or ratio in nature and normally distributed, extraction from a Pearson r correlation matrix produces results analogous to those from a Spearman Rho correlation matrix.