[<< wikibooks] Cognitive Science: An Introduction/Statistics
== Factor Analysis ==
When we're trying to understand the mind, and how it works, one of the things we want to know is how we can think of the different parts of the mind. Keep in mind that this might be a different question from the different parts of the brain--there are likely functions in the mind that are not restricted to a particular location, much like a function in a company might not be strongly associated with a specific, few rooms in a building. 
One popular way to try to understand the different parts of the mind is by using a statistical technique called "factor analysis" (in other fields it is known as "principle components analysis.") What factor analysis does is look for relationships between large numbers of variables (typically, scores of different kinds of questions on a written test). Suppose you had a 200 question test given to 1000 people. Some of these questions might involve questions about world history, and others might test algebra abilities. We might expect that people who did well on world history question A might also do well on world history question B. Likewise, we might not expect whether somebody got A right will also get a math question right. We might expect a factor analysis to look at all of these questions, and the patterns of correct and incorrect answers given, and find two "factors." The scientist will then look at what questions belong in which factors and notice that some are about history and some are about math, and name the factors "history" and "math." You can think of it as a way of reducing the number of variables--in this case, 200 questions to 2 factors. A factor is the weighted sum of the variables. A math question would be called a "marker" for the math factor, and "load" on that factor. In psychology, we tend to interpret factors as representations of underlying abilities.
This is what's called an "exploratory factor analysis." It's exploratory because we basically just give the data to the technique and it returns the patterns it found. We don't use our pre-conceived hypotheses about the structure in the data. A problem with exploratory factor analyses is that there are several ways to do it, and depending on which way you do it, you can get different factors, and different numbers of factors. Often the choice of technique is subjective. 
If a scientist already has an idea of the structure of the data (that is, what she thinks the factors might be), then she can run a "confirmatory factor analysis," which tests whether the factors she thinks are there really are. Some have argued that this is a better way to do science, and is able to find evidence against theories in a way that exploratory factor analysis cannot.