Facets: See generalizability theory.

Factor: A term used in a variety of ways in statistics. Most commonly, it refers to a categorical variable with a small number of levels under investigation in an experiment as a possible source of variation in a response variable, i.e. simply a categorical explanatory variable. Also used for the latent variables identified in a factor analysis.

Factor analysis: A collection of techniques for investigating the correlation matrix or variance―covariance matrix between a set of variables to determine whether the correlation or covariances between the observed or manifest variables can be explained by assuming that the latter are related to a small number of underlying, unobservable latent variables, or common factors. More specifically, each measured variable is assumed to be a linear function of the common factors plus a residual term known in this context as a specific factor. The coefficients defining the common factors are known as factor loadings. A very early example of the application of the methodology postulated that the scores of individuals on a number of cognitive tests could be decomposed to a general factor common to all variables, which might be labelled general intelligence, and a specific factor, which was different for each variable. There are essentially two approaches to factor analysis that need to be differentiated carefully: the first, exploratory factor analysis, imposes no constraints on the structure of the common factors, whereas the second, confirmatory factor analysis, imposes constraints; in particular, it sets specific factor loadings to zero in line with some theoretical factor structure to be tested on the current data.