*Section author: Danielle J. Navarro and David R. Foxcroft*

# Factor AnalysisΒΆ

Previous chapters have covered statistical tests for differences between
two or more groups. However, sometimes when conducting research, we may
wish to examine how multiple variables *co-vary*. That is, how they are
related to each other and whether the patterns of relatedness suggest
anything interesting and meaningful. For example, we are often
interested in exploring whether there are any underlying unobserved
**latent factors** that are represented by the observed, directly
measured, variables in our dataset. In statistics, latent factors are
initially hidden variables that are not directly observed but are rather
inferred (through statistical analysis) from other variables that are
observed (directly measured).

In this chapter we will consider a number of different Factor Analysis and related techniques, starting with Exploratory Factor Analysis (EFA). EFA is a statistical technique for identifying underlying latent factors in a data set. In the next section, we will cover Principal Component Analysis (PCA) which is a data reduction technique which, strictly speaking, does not identify underlying latent factors. Instead, PCA simply produces a linear combination of observed variables. Following this, the section Confirmatory Factor Analysis (CFA) shows that, unlike EFA, with CFA you start with an idea - a model - of how the variables in your data are related to each other. You then test your model against the observed data and assess how good a fit the model is. Finally, we introduce Internal consistency reliability analysis which tests how consistently a scale measures a psychological construct.