Factor analysis and principal component analysis (PCA) are techniques for identifying clusters of variables. These techniques have three uses: understanding the structure of a set of variables (1), construct a questionnaire to measure an underlying variable (2) and reduce a dataset to a more manageable size while retaining as much of the original information as possible (3). Factor analysis attempts to achieve parsimony by explaining the maximum amount of common variance in a correlation matrix using the smallest number of explanatory constructs (latent variables). PCA attempts to explain the maximum amount of total variance in a correlation matrix by transforming the original variables into linear components. A factor loading refers to the coordinate of a variable along a classification axis (e.g. Pearson correlation between factor and variable). It tells us something about the relative contribution that a variable makes to a factor. In factor analysis, scores on the measured variables are predicted from the means of those variables plus a person’s scores on the common factors (e.g. factors that explain the correlations between variables) multiplied by their factor loadings, plus scores on any unique factors within the data (e.g. factors that cannot explain the correlations between variables). In PCA, the components are predicted from the measured variables. One major assumption of factor analysis is that the algebraic factors represent real-world dimensions. A regression technique can be used to predict a person’s score on a factor. Using this technique, the resulting actor scores have a mean of 0 and a variance equal to the squared multiple correlation between the estimated factor scores and the true factor values. A downside is that the scores can correlate with other factor scores from a different orthogonal factor. The Bartlett method and the Anderson-Rubin method can be used to overcome this problem. The Bartlett method produces...