On establishing that pathology scores are quantitative

Abstract

Psychopathology researchers, like other scale developers, often fail to establish that underlying pathology scores are quantitative, concentrating instead on construction of numeric assignment procedures. By doing so, researchers risk that there may be no qualitative data relations that correspond to the quantitative structure inherent in the numerical assignment. Without representational data correspondence, numbers and their operations are devoid of meaning in a measurement context. As a basis for quantitative establishment, a logic of quantification is presented. Pathology as a medical condition is presumed to exist in amounts referred to as magnitudes. A theory of measurable magnitudes is offered founded on seven axioms of quantity. The central conclusion from a measurement perspective is that for any ratio of two magnitudes of the same pathology, a / b , there exists a corresponding rational measure-number. If magnitude b is a unit of measurement, then the measure-number is the number of measure units contained in magnitude a . Thus, measurement is definable as the act of determining the measure-number corresponding to a target magnitude a given a unit of measurement b . The utility of the definition, however, depends upon the extent to which observable data support the quantitative hypothesis. A test that pathology scores are quantitative is provided. If supported, pathology scores can be treated as numeric in subsequent analyses.