Factor analysis examine the patterns of correlations between observed variables. If a set of variables are highly correlated, they are likely influenced by the same factor. If variables are not highly correlated they are probably influenced by different factors. Unlike Exploratory Factor Analysis (EFA), which tries to uncover the nature of factors that influence a set of variables, CFA tests whether or not a specified set of factor influence variables in a theorized way.
Factor analysis was first developed in 1904 by British psychologist Charles Spearman, who used the method to confirm his two-factor theory of intelligence. His theory stated that the high correlation between school childrens' scores on a variety of subjects was due to the underlying factors of mental ability. Although his method was not originally referred to as CFA, it was confirmatory in nature by seeking to test a given hypothesis about the structure relating factors and variables instead of trying to discover the underlying structure.
Although originally used in the pursuit of intelligence research in psychology, CFA became popular in other fields such as education, physical sciences and marketing in the late 1960s. In education, CFA is used in the development of state tests to ensure that each question tests one or more educational standards. In marketing, CFA can be used to determine if survey questions that are seemingly very similar but vary in small ways do, in fact, test the same construct. CFA is also used in groundwater quality management to test if chemical signatures are coming from expected sources.
A general advantage of factor analysis lies in the reduction of the overall number of variables used to explain outcomes. For example, a state test might have over 100 questions testing different concepts. By boiling each of these questions down to its corresponding state standard, the factor "state standard" can be used as a variable instead of each question in further research. More variables require a larger sample size, which is often difficult to find in education research. CFA can also be useful when developing surveys by allowing the researcher to reduce the number of questions in the survey without losing information.
Although CFA tests a hypothesized structure for a set of variables, it does not necessarily mean that the structure is true. There may be another equally valid structure for the same set of variables. In addition, CFA requires a larger sample size than EFA, because it produces inferential statistics, which is used to draw conclusions about a population from only a sample of the population.