Counting and quantification: Comparing psychometric and metrological perspectives on visual perceptions of number

In gaining a better understanding of how to characterise human response, essential to improved person-centred care and other situations where human factors are crucial, recent work has attempted to link metrological (resolution, classification effectiveness) and psychometric (Rasch) characterisation of Man as a Measurement Instrument. The present work offers a more detailed account of these investigations following our first preliminary conference report, continuing a study of elementary tasks, such as counting dots, where one knows independently the expected value because the measurement object (collection of dots) is prepared in advance. The analysis is compared and contrasted with recent approaches to this problem by others, for instance using signal error fidelity and loss functions. Independent sources of measurement uncertainty, such as under-estimation of scores, are distinguished from separate estimates of task challenge and individual counting ability, and accounted for in estimates of reliability of the various measures.