This chapter introduces more advanced statistical techniques by providing some specific examples; the techniques themselves will not be presented because the intent is to help the reader identify when one of these techniques is appropriate for a given research question. Methodologies covered include factor analysis, cluster analysis, discriminant function analysis, and multidimensional scaling.

*Factor Analysis* (FA) uses standardized
variables to reduce data sets using *Principal Components
Analysis* (PCA), the most widely used data reduction
technique. It is based on an *orthogonal
decomposition* of an input matrix to yield an output matrix
that consists of a set of orthogonal components (or factors) that
maximize the amount of variation in the variables from the input matrix.
In turn, the process almost always produces a smaller, compact number of
output components. In linear algebra terms, PCA works from the
covariance matrix to produce a set of eigenvectors and eigenvalues. The
components in the output matrix are linear combinations of the input
variables, where the first component maximizes the variance captured,
and with each subsequent factor capturing as much of the residual
variance as possible, while taking on an uncorrelated direction in
space. A more general version of PCA is *Hotelling’s Canonical
Correlation Analysis* (CCA), which—assuming multivariate normality—can be used to test whether two sets of variables are independent. ...

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