Statistics Toolbox

Comparison of Factor Analysis and Principal Components Analysis

There is a good deal of overlap in terminology and goals between Principal Components Analysis (PCA) and Factor Analysis (FA). Much of the literature on the two methods does not distinguish between them, and some algorithms for fitting the FA model involve PCA. Both are dimension-reduction techniques, in the sense that they can be used to replace a large set of observed variables with a smaller set of new variables. However, the two methods are different in their goals and in their underlying models. Roughly speaking, you should use PCA when you simply need to summarize or approximate your data using fewer dimensions (to visualize it, for example), and you should use FA when you need an explanatory model for the correlations among your data.

Predicting Factor Scores

Multivariate Analysis of Variance (MANOVA)