Discrete ordinal & interval scaling and psychometrics

SP Technical Research Institute of Sweden, Measurement Technology, Box 857, S-501 15 Borås, Sweden

^a Corresponding author: leslie.pendrill@sp.se

Abstract

Reliable decisions about conformity of product in many ‘person-centred’ domains of contemporary interest based on measurement require the comparability and risk assessment associated with metrological quality assurance – in terms of traceability and measurement uncertainty. But in qualitative and subjective measurement, these metrological concepts are in their infancy. Challenges include the failure of many common tools of statistics on the ordinal scales typical of ‘human’ measurement. Measurable constructs for perceptual characteristics such as task challenge or the quality of a service, matched by the corresponding human ability and satisfaction for these items, respectively, have also to be formulated, as is done increasingly with psychometric approaches, such as Rasch and Prospect Theory. To aid basic understanding in this relatively new field of metrology, some of the most elementary perceptions, e.g. the simple observation of clouds of dots, will be analysed in the present work where metrics for the location and dispersion of data on discrete scales, including impact, will be linked via instrumental bias and resolution, to psychometric measures of the ability to perform a series of tasks of increasing difficulty.