# Factor Analysis

The main applications of factor analytic techniques are 1) to reduce the number of variables and 2) to detect structure in the relationships between variables, that is to classify variables. Therefore, factor analysis is applied as a data reduction or (exploratory) structure detection method (the term factor analysis was first introduced by Thurstone, 1931, although similar techniques were used by Spearman as early as 1904 in his classic research on the nature of intelligence).

For example, suppose we want to measure people's satisfaction with their lives. We design a satisfaction questionnaire with various items; among other things we ask our subjects how satisfied they are with their hobbies (item 1) and how intensely they are pursuing a hobby (item 2). Most likely, the responses to the two items are highly correlated with each other. Given a high correlation between the two items, we can conclude that they are quite redundant.

One can summarize the correlation between two variables in a scatterplot. A regression line can then be fitted that represents the "best" summary of the linear relationship between the variables. If we could define a variable that would approximate the regression line in such a plot, then that variable would capture most of the "essence" of the two items. Subjects' single scores on that new factor, represented by the regression line, could then be used in future data analyses to represent that essence of the two items. In a sense we have reduced the two variables to one factor.

Factor Analysis is an exploratory method; for information in Confirmatory Factor Analysis, see SEPATH. For more information on Factor Analysis, see the Factor Analysis Overviews.