The Data Analytic Implications of Human Psychology's Dimensions Being Ordinally Scaled

Abstract

Scientific findings involve description, and description requires measurements on the dimensions descriptive of the phenomena described. The richer a description the more multidimensional is the abstract space in which that description in effect locates what is described. Many of the dimensions of human psychological phenomena, including those of psychotherapy, are naturally gradated only ordinally. So descriptions of these phenomena locate them in merely ordinal hyperspaces, which imposes severe constraints on data analysis for inducing or testing explanatory theory involving them. Therefore, it is important to be clear about what these constraints are and so what properly can be concluded on the basis of ordinal-scale multivariate data, which also provides a test for methods that are proposed to transform ordinal-scale data into ratio-scale data (e.g., classical test theory, item response theory, additive conjoint measurement), because such transformations must not violate these constraints and so distort descriptions of studied phenomena.