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Statistics in a Nutshell by Sarah Boslaugh, Paul Andrew Watters

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Chapter 16. Other Statistical Techniques

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

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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