The paper is a critique of the traditional mode of interpreting factor analyses; it is not a criticism of factor analysis per se. Instead, the author proposes a statistical procedure based upon stepwise regression (SRP). The traditional mode focuses on the largest factor loadings (FL). A factor is both described and named by these heavily weighted variables. This method is based on a covert assumption that a factor has a sufficient degree of internal-consistency which is housed in the highly loaded variables. The assumption needs to be tested in every factor. By its very nature, the SRP tests that assumption. Within the SRP, correlations of factor scores with the variables produce the FL's (step 0). At the other end, the multiple regression of all the variables produces a column of unique variance factor-coefficients. The intervening SRP steps provide descriptions of the factors. FL's can enter into many types of configurations. Some examples of the complexity are presented in the paper. A factor is usually composed of several sources of unique and common variances. The traditional method irons out this complexity into a fictitious "oneness." The SRP presents the factor in terms of its independent configurations. (Author)