Michell has argued that item response models carry an inherent paradox because they incorporate error. In counter-arguments, the paradox has been dismissed based on the claim that such models need to incorporate error terms. It has also been claimed that item response models use information contained within intervals. The aim is to describe a formal connection in item response models between error and the measurement unit. It is argued that given the connection, Michell’s criticisms are not as easily dismissed as some claim: His argument does raise questions about whether item response theory can be used to measure psychological attributes. On the other hand, Michell’s position offers little in the way of guidance about how to approach the scientific task of quantification. For this reason, the theoretical framework that he adopts is also critically examined with a particular focus on the way in which measurement in physics is approached.
AndrichD. (2003). On the distribution of measurements in units that are not arbitrary. Social Science Information, 42, 557–589.
2.
BerkaK. (1982). Measurement: Its concepts, theories, and problems (RiskaA., Trans.). (Boston studies in the philosophy of science, 72.) Dordrecht, The Netherlands: Reidel.
3.
BirnbaumA. (1968). Some latent trait models and their use in inferring an examinee’s ability. In LordF. M.NovickM. R. (Eds.), Statistical theories of mental test scores (pp. 397–472). Reading, MA: Addison-Wesley.
4.
BlackJ. (1806). Expansion-thermometers. In RobisonJ. (Ed.), Lectures on the elements of chemistry (Vol. 1, pp. 49–59). Philadelphia, PA: printed for Mathew Carey by B. Graves.
5.
BorsboomD.MellenberghG. J. (2004). Why psychometrics is not pathological: A comment on Michell. Theory & Psychology, 14, 105–120.
6.
BorsboomD.MellenberghG. J.Van HeerdenJ. (2004). The concept of validity. Psychological Review, 111, 1061–1071.
7.
Bureau International des Poids et Mesures (BIPM). (2008). International vocabulary of metrology—Basic and general concepts and associated terms (VIM). General Conference on Weights and Measures. Retrieved from http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
8.
ChangH. (1995). Circularity and reliability in measurement. Perspectives on Science, 3, 153–172.
9.
ChangH. (2004). Inventing temperature. Oxford, UK: Oxford University Press.
10.
de BoerJ. (1994/1995). On the history of quantity calculus and the international system. Metrologia, 31, 405–429.
11.
EmersonW. H. (2004). On the algebra of quantities and their units. Metorologia, 45, 134–138.
12.
HebraA. J. (2010). The physics of metrology—All about instruments: From trundle wheels to atomic clocks. New York, NY: Springer.
13.
HumphryS. M. (2010). Modeling the effects of person group factors on discrimination. Educational and Psychological Measurement, 70, 215–231.
14.
HumphryS. M. (2011). The role of the unit in physics and psychometrics. Measurement: Interdisciplinary Research and Perspectives, 9, 1–24.
15.
HumphryS. M.AndrichD. (2008). Understanding the unit in the Rasch model. Journal of Applied Measurement, 9, 249–264.
16.
KrantzD. H.LuceR. D.SuppesP.TverskyA. (1971). Foundations of measurement (Vol. 1). New York, NY: Academic Press.
17.
KyburgH. E.Jr(1997). Quantities, magnitudes, and numbers. Philosophy of Science, 64, 377–410.
18.
LangmuirI.HallR. N. (1989). Pathological science. Physics Today, 42(10), 36–48.
19.
MasseyB. S. (1971). Units, dimensional analysis and physical similarity. London, UK: Van Nostrand Reinhold.
20.
MichellJ. (1993). The origins of the representational theory of measurement: Helmholtz, Hölder, and Russell. Studies in History and Philosophy of Science, 24, 185–206.
21.
MichellJ. (1997). Quantitative science and the definition of measurement in psychology. British Journal of Psychology, 88, 355–383.
22.
MichellJ. (1999). Measurement in psychology. Cambridge, UK: Cambridge University Press.
23.
MichellJ. (2005). The logic of measurement: A realist overview. Measurement, 38, 285–294.
24.
MichellJ. (2007). Measurement. In TurnerP. T.MarkW. R. (Eds.), Handbook of the philosophy of science (pp. 71–119). Amsterdam, The Netherlands: Elsevier.
25.
MichellJ. (2008). Is measurement pathological science?Measurement: Interdisciplinary Research and Perspectives, 6, 7–24.
26.
RaschG. (1980). Probabilistic models for some intelligence and attainment tests (WrightB. D., fore-and afterword; expanded ed.). Chicago, IL: University of Chicago Press. (Original work published 1960)
27.
SherryD. (2011). Thermoscopes, thermometers, and the foundations of measurement. Studies in History and Philosophy of Science, 42, 509–524.
28.
SijtsmaK. (2012). Psychological measurement between physics and statistics. Theory & Psychology, 22, 786–809. doi: 10.1177/0959354312454353
29.
StevensS. S. (1946). On the theory of scales and measurement. Science, 103, 667–680.
30.
TrendlerG. (2009). Measurement theory, psychology and the revolution that cannot happen. Theory & Psychology, 19, 579–599.
31.
Van der LindenW. J. (1994). Fundamental measurement and the fundamentals of Rasch measurement. In WilsonM. (Ed.), Objective measurement: Theory into practice (Vol. 2, pp. 3–24). Norwood, NJ: Ablex.
