Functions of units, scales and quantitative data: Fundamental differences in numerical traceability between sciences

Abstract Quantitative data are generated differently. To justify inferences about real-world phenomena and establish secured knowledge bases, however, quantitative data generation must follow transparent principles applied consistently across sciences. Metrological frameworks of physical measurement build on two methodological principles that establish transparent, traceable—thus reproducible processes for assigning numerical values to measurands. Data generation traceability requires implementation of unbroken, documented measurand-result connections to justify attributing results to research objects. Numerical traceability requires documented connections of the assigned values to known quantitative standards to establish the results' public interpretability. This article focuses on numerical traceability. It explores how physical measurement units and scales are defined to establish an internationally shared understanding of physical quantities. The underlying principles are applied to scrutinise psychological and social-science practices of quantification. Analyses highlight heterogeneous notions of ‘units’ and ‘scales’ and identify four methodological functions; they serve as (1) ‘instruments’ enabling empirical interactions with study phenomena and properties; (2) structural data format; (3) conceptual data format; and (4) conventionally agreed reference quantities. These distinct functions, employed in different research stages, entail different (if any) rationales for assigning numerical values and for establishing their quantitative meaning. The common numerical recoding of scale categories in tests and questionnaires creates scores devoid of quantitative information. Quantitative meaning is created through numeral-number conflation and differential analyses, producing numerical values that lack systematic relations to known quantity standards regarding the study phenomena and properties. The findings highlight new directions for the conceptualisation and generation of quantitative data in psychology and social sciences.