# Factor Analysis

Factor Analysis is a procedure that seeks to determine a reduced number of variables, called factors, that explain much of the variation present in a larger number of measured variables. For example Factor Analysis of the results of a questionnaire given to students may reveal that groups of questions relating to differences in mechanical and artistic ability are important in influencing the choice of career path. If so, these groups of questions would come out as separate factors, a factor comprised mainly of the results of mechanical ability questions and another based on the artistic questions.

statistiXL provides a comprehensive module for Factor Analysis, with a variety of analytical options. Data can be input as either raw values or pre-calculated correlation or covariance matricies. Either the correlation or covariance matrix can be used in calculating the factors. The number of factors to be extracted can be established by several different criteria: 1) the number of factors can be chosen to encompass a specified percentage of the total variance in the original data, 2) you can choose to extract factors with eigenvalues greater than a set value, 3) you can extract a specific number of factors. A variety of methods are included for determining the factors including the principal component method (not to be confused with principal component analysis), principal factor method and maximum likelihood method. The axes of the resulting factors can then be rotated to improve the factor structure using either Varimax, Quartimax, Equamax or Promax procedures.

Results are presented in tabular form. Descriptive statistics and the correlation or covariance matrix are provided, if these options were selected. Eigenvalues are then listed, along with the percent and cumulative percent of the variation in the original data that they encompass. Communalities are then given for each extracted factor. Unrotated factor loadings (and rotated loadings if selected) are listed, along with case-wise factor scores. Scree plots, loading plots and factor plots are produced if these options are selected.

The help file included with statistiXL provides an overview of factor analysis, and an example of factor analysis using the principal component method, with rotation.