Is Error Fatal to Interval Measurement?

Norman Cliff: "One is dubious that any convincing evidence exists, such as provided by conjoint measurement, that would allow the equating of intervals along the [raw] score variable. Either it is treated ordinally, or as a pro forma interval scale. There exist, of course, models that attempt to convert the ordinal test data provided by test items into some more strictly defined scale (e.g., Birnbaum, 1968; Lord & Novick, 1968; Rasch, 1966), but the evidence that supports the interval-scale status of the derived variables is not compelling because of the amount of error involved." (1993, p.87)

Cliff here takes the position that interval-scaling must be proved empirically, which was Norman Campbell's argument as to why fundamental measurement can't exist in the social sciences, summarized as "you can't concatenate heads." But Cliff makes the point with physical measurement (p. 62) that "measuring length is much more effectively and efficiently done if it is embedded in a larger system, in this instance the science of geometry." For social science measurement, the larger system is algebra. With algebra, it is easy to demonstrate that, however error-ridden the empirical data and however great the error in the resultant measures, there is only one method of transforming ordinal data that accords with conjoint measurement and so can possibly produce interval scales, the Rasch model.

Once the hurdle of interval scaling is overcome, social science can then advance in the same way as has physical science. "What is clear about physical measurement is its intimate entanglement with the science itself. Somehow, someone hits upon a way of taking observations that results in regular relations of a quantifiable sort. Someone else finds a way of making observations that are highly correlated with the first sort, but whose relations are even more precise. It is thus that empirical variables are defined operationally and theoretical variables are born" (p. 63).

John Michael Linacre

Cliff, N. (1993) What is and isn't measurement. In G. Keren & C. Lewis (Eds.), A Handbook for Data Analysis in the Behavioral Sciences: Methodological Issues. Hillsdale, NJ: Lawrence Erlbaum Assoc.

Is Error Fatal to Interval Measurement? Cliff, N. … Rasch Measurement Transactions, 1999, 13:3 p. 702

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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