STATISTICAL AND PSYCHOMETRIC INFERENCE IN PRINCIPAL COMPONENTS ANALYSIS

Statistical inference applied to principal components analysis deals with estimating the parameters of the correlation matrix, R, found in the population, from the characteristics of the sample matrix, R*. On the other hand, psychometric inference refers to estimating the internal consistency of the components themselves, so that the decisions about retaining a component for further analysis can be based upon psychometric criteria. A slightly modified approach to statistical inference, which focuses upon the variance of the Components in the population, has been suggested. This viewpoint can be extended to estimating the true score variance and the reliabilities of the components in the population of subjects. Psychometric tests of significance can then be made statistical in nature.