Applications of standard error estimates in unrestricted factor analysis: significance tests for factor loadings and correlations.

Estimates of standard errors of factor loadings and factor correlations in the unrestricted factor analysis model can be computed for oblique or orthogonal solutions under maximum likelihood. This information can be used to test individual coefficients for significance, to evaluate whether an orthogonal or oblique structure is most consistent with sample data, or to compute confidence intervals for single parameters or confidence regions for arbitrary groups of coefficients. Because the number of parameters estimated in factor analysis is approximately the product of number of variables multiplied by number of factors, a Bonferroni correction for the critical point of the individual test statistics is recommended to control the probability of a Type I error. Several examples are presented.