PRINCIPAL COMPONENTS AND THE MAXIMUM LIKELIHOOD METHODS AS TOOLS TO ANALYZE LARGE DATA WITH A PSYCHOLOGICAL TESTING EXAMPLE

Abstract

Basing on the study of correlations between large numbers of quantitative variables, the method factor analysis (FA) aims at finding structural anomalies of a communality composed of p-variables and a large number of data (large sample size). It reduces the number of original (observed) variables by calculating a smaller number of new variables, which are called factors (Hair, et al., 2010). This paper overviews the factor analysis and their application. Here, the method of principal components analysis (PCA) to calculate factors with Varimax rotation is applied. The method of maximum likelihood with Quartimax rotation is used for comparison purposes involving the statistic package SPSS. The results clearly report the usefulness of multivariate statistical analysis (factor analysis). The application is done by a set of data from psychological testing (Revelle, 2010).