The key statistics associated with factor analysis are as follows:
Bartlett’s test of sphericity. Bartlett’s test of sphericity is a test statistic used to examine the hypothesis that the variables are uncorrelated in the population. In other words, the population correlation matrix is an identity matrix; each variable correlates perfectly with itself (r = I) but has no correlation with the other variables (r = 0).
Correlation matrix. A correlation matrix is a lower triangle matrix showing the simple correlations, r. between all possible pairs of variables included in the analysis. The diagonal elements, which are all I, are usually omitted.
Communality. Communality is the amount of variance a variab\e there with all the other variables being considered. This is also the proportion of variance explained by the common factors
Eigenvalue. The eigenvalue represents the total variance explained by each factor. Factor loadings. Factor loadings are simple correlations between the variables and the factors. Factor loading plot. A factor loading plot is a plot of the original variables using the factor loadings as coordinates.
Factor matrix. A factor matrix contains the factor loadings of all the variables on all the factors extracted.
Factor scores. Factor scores are composite scores estimated for each respondent on the derived factors
Factor scores coefficient matrix. This matrix contains the weights, or factor score coefficients, used to combine the standardized variables to obtain factor scores .
Kaiser-Meyer-Olkin (KMOj measure of sampling adequacy. The Kaiser-Meyer-Olkin (KMO) measure of samplint.(dequacy is an index used to examine the appropriateness of factor analysis. High values (between 0.5 and 1.0) indicate factor analysis is appropriate. Values below 05 imply that factor analysis may not be appropriate.
Percentage of variance. This is the percentage of the total variance attributed to each factor
Residuals. Residuals are the differences between the observed correlations, as given in the input correlation matrix, and the reproduced correlations, as estimated from the factor matrix.
Scree plot. A scree plot is a plot of the eigenvalues against the number of factors in order of extraction.
In the next section, we describe the uses of these statistics in the context of the procedure for conducting factor analysis.