This paper demonstrates how Q-methodology combines artistic and scientific procedures to allow social science researchers to develop and test theories about differences in persons. Q-methodology is based on factor analysis. In R-technique factor analysis, the most commonly used technique, variables define the columns and persons define the rows of the raw data matrix used to create the factored matrix of associations. In Q-technique factor analysis, the same two dimensions are used, although they are reversed. Q-methodology has sometimes been referred to as transposed analysis or inverse analysis. Because it is based on theoretically driven assumptions and computed using complex factor analytic procedures, Q-analysis serves as a fine example of the science of research, but its focus on small samples, intra-individual attitudes, and the researcher's creativity in identifying the emergent person factors yielded by the analysis make it a highly artistic technique as well. Over 1,500 studies using Q-methodology can be found in the social science literature. Its contribution to behavioral research has been recognized. One figure gives an example of an unnumbered graphic scale, and a 57-item list of references is included. (SLD)