Abstract

A study of elementary counting (of simple clouds of dots by the Munduruku indigenouspeople of Brazil) is reanalysed in order to compare and contrast three kinds of probabilitymass functions (PMFs): (i) quantitative response to a discrete range of counts; (ii) the classicPoisson distribution of miscounts; and (iii) psychometric (Rasch) distributions of countingtask difficulty and person counting ability. This reanalysis highlights how best to handlePMFs which provide a means of defining—for discrete and qualitative data—the basicmetrics, viz. location and dispersion, of metrology—quality-assured measurement, asincreasingly required since the turn of the millennium in topical and challenging qualityassuranceapplications, amongst others, in the human sciences and in Artificial Intelligence.PMF-based metrics, useful in ’clinical’ and other applications where meaning and valueare sought, complement the traditionally dominating role played by the correspondingprobability density functions (PDF) in ’analytical’, quantitative and continuous Metrologyin Physics. New insights are provided when benchmarking the Rasch Poisson CountsModel, which has received less attention in modern metrology, against full psychometricRasch modelling.

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