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Reliability coefficients indicate the proportion of total variance attributable to differences among measures separated along a quantitative continuum by a testing, survey, or assessment instrument. Reliability is usually considered to be influenced by both the internal consistency of a data set and the number of items, though textbooks and research papers rarely evaluate the extent to which these factors independently affect the data in question. Probabilistic formulations of the requirements for unidimensional measurement separate consistency from error by modelling individual response processes instead of group-level variation. The utility of this separation is illustrated via analyses of small sets of simulated data, and of subsets of data from a 78-item survey of over 2,500 parents of children with disabilities. Measurement reliability ultimately concerns the structural invariance specified in models requiring sufficient statistics, parameter separation, unidimensionality, and other qualities that historically have made quantification simple, practical, and convenient for end users. The paper concludes with suggestions for a research program aimed at focusing measurement research more on the calibration and wide dissemination of tools applicable to individuals, and less on the statistical study of inter-variable relations in large data sets. © 2010 IOP Publishing Ltd.

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