Factor analysis is a method of data investigation that allows a researcher to simplify her data in an orderly manner. The entire workings of factor analysis rely on mathematical methods and statistical measures that describe the interrelationships of the variables involved in the analysis. Natural, applied and behavioral sciences all make heavy use of factor analysis for the purpose of discovering how variables mutually vary and whether they form patterns.
Since the correlation coefficient is the basic statistic in factor analysis, you can perform factor analysis by using the geometrical method. The basic idea behind the geometrical method is to represent the correlation in a scattergram. A scattergram is a visual way of describing and checking the relationships between variables. This method is feasible for small factor analysis studies because each set of variables can be compared, yielding you a set of correlations. This method saves you the complication of dealing with correlation matrices and vectors.
The main purpose of exploratory factor analysis is to assist the researcher in producing a hypothesis in his study. Exploratory factor analysis works by identifying variables, describing their interrelationships, and then classifying the variables into factor loadings. In this way, the researcher can analyze the complex web of variables and arrive at a hypothesis of how those variables relate to each other.
Confirmatory factor analysis works on the assumption that the researcher has already developed a theory from other sources, perhaps including other methods of factor analysis. From this standpoint, confirmatory factor analysis helps the researcher create models for her theory. This form of factor analysis begins with a set of relevant data and results in a factor structure. The researcher then uses the factor structure to validate, falsify or modify her model, depending on how well the data fit.