A factor analysis is utilized to discover factors among observed variables or 'latent' variables. Similarly stated, if a data set contains an overwhelming number of variables, a factor analysis may be performed to reduce the number of variables for analysis. A factor analysis will group similar variables, producing a set of factors, or compiled variables, to use for further analysis. A statistical analysis software package will be instrumental in the Factor Analysis calculation. Examples of statistical analysis packages are SPSS and SAS.
Generate a correlation matrix on the data set. A correlation matrix is a table of correlation coefficients. A correlation coefficient is the quantifying unit of correlation. This number expresses the direction and strength of a linear relationship measured between two random variables.
Establish baselines for desired factors (compiled variables). For example, if the data collection instrument is a survey and responses are measured from 1 -- Least Desirable Outcome to 10 -- Most Desirable Outcome, values of 8, 9 and 10 may be examined and the corresponding variables grouped according to similarities to create factors.
Rotate factors to maximize the linear relationships between factors and variables. For this function, the statistical application demonstrates its value. The number of manual calculations required would be massive on a large data set.
Generate and print the Output report. The Output report will include the following sections: Descriptive Statistics, the Correlation Matrix, Kaiser-Meyer-Olkin and Bartlett's Test, Communalities, a Scree Plot, a Factor Matrix and a Rotated Factor Matrix.
Interpret the output from the statistical application based on intuitive knowledge of the data and empirical questions to be answered.