I’d like to revisit the distinction between measurement models and statistical models. Rasch was well known for joking about burning all books containing the words “normal distribution” (Andersen, 1995, p. 385). Rasch’s book and 1961 article both start on their first pages with a distinction between statistical models describing intervariable relations at the group level and measurement models prescribing intravariable relations at the individual level. I think confusion between these kinds of models has caused huge problems.

We typically assume all statistical analyses are quantitative. We refer to any research that uses numbers as quantitative even when nothing is done to map a substantive and invariant unit on a number line. We distinguish between qualitative and quantitative data and methods as though quantification has ever been achieved in the history of science without substantive qualitative understandings of the constructs.

Quantification in fact predates the emergence of statistics by millennia. It seems to me that there is a great deal to be gained from maintaining a careful distinction between statistics and measurement. Measurement is not primarily performed by someone sitting at a computer analyzing data. Measurement is done by individuals using calibrated instruments to obtain immediately useful quantitative information expressed in a universally uniform unit.

Information overload is one of the big topics of the day. Which will contribute more to reducing that overload in efficient and meaningful ways: calibrated instruments measuring in common units giving individual users immediate feedback that summarizes responses to dozens of questions, or ordinal group-level item-by-item statistics reported six months too late to do anything about them?

Instrument calibration certainly makes use of statistics, and statistical models usually assume measurement has taken place, but much stands to be gained from a clear distinction between inter- and intra-variable models. And so I respectfully disagree with those who assert that “the Rasch model is first of all a statistical model.” Maxwell’s method of making analogies from well known physical laws (Nersessian, 2002; Turner, 1955) was adopted by Rasch (1960, pp. 110-115) so that his model would have the same structure as the laws of physics.

Statistical models are a different class of models from the laws of physics (Meehl, 1967), since they allow cross-variable interactions in ways that compromise and defeat the possibility of testing the hypotheses of constant unit size, parameter separation, sufficiency, etc.

I’d like to suggest a paraphrase of the first sentence of the abstract from a recent paper (Silva, 2007) on using analogies in science education: Despite its great importance, many students and even their teachers still cannot recognize the relevance of measurement models to build up psychosocial knowledge and are unable to develop qualitative explanations for mathematical expressions of the lawful structural invariances that exist within the social sciences.

And so, here’s a challenge: we need to make an analogy from Silva’s (2007) work in physics science education and develop a curriculum for social science education that follows a parallel track. We could trace the development of reading measurement from Rasch (1960) through the Anchor Test Study (Jaeger, 1973; Rentz & Bashaw, 1977) to the introduction of the Lexile Framework for Reading (Stenner, 2001) and its explicit continuity with Rasch’s use of Maxwell’s method of analogy (Burdick, Stone, & Stenner, 2006) and full blown predictive theory (Stenner & Stone, 2003).

With the example of the Rasch Reading Law in hand, we could then train students and teachers to think about structural invariance in the context of psychosocial constructs. It may be that, without the development and dissemination of at least a college-level curriculum of this kind, we will never overcome the confusion between statistical and measurement models.

References

Andersen, E. B. (1995). What George Rasch would have thought about this book. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 383-390). New York: Springer-Verlag.

Burdick, D. S., Stone, M. H., & Stenner, A. J. (2006). The Combined Gas Law and a Rasch Reading Law. Rasch Measurement Transactions, 20(2), 1059-60 [http://www.rasch.org/rmt/rmt202.pdf].

Jaeger, R. M. (1973). The national test equating study in reading (The Anchor Test Study). Measurement in Education, 4, 1-8.

Meehl, P. E. (1967). Theory-testing in psychology and physics: A methodological paradox. Philosophy of Science, 34(2), 103-115.

Nersessian, N. J. (2002). Maxwell and “the Method of Physical Analogy”: Model-based reasoning, generic abstraction, and conceptual change. In D. Malament (Ed.), Essays in the history and philosophy of science and mathematics (pp. 129-166). Lasalle, Illinois: Open Court.

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests (Reprint, with Foreword and Afterword by B. D. Wright, Chicago: University of Chicago Press, 1980). Copenhagen, Denmark: Danmarks Paedogogiske Institut.

Rasch, G. (1961). On general laws and the meaning of measurement in psychology. In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (pp. 321-333 [http://www.rasch.org/memo1960.pdf]). Berkeley, California: University of California Press.

Rentz, R. R., & Bashaw, W. L. (1977, Summer). The National Reference Scale for Reading: An application of the Rasch model. Journal of Educational Measurement, 14(2), 161-179.

Silva, C. C. (2007, August). The role of models and analogies in the electromagnetic theory: A historical case study. Science & Education, 16(7-8), 835-848.

Stenner, A. J. (2001). The Lexile Framework: A common metric for matching readers and texts. California School Library Journal, 25(1), 41-2.

Stenner, A. J., & Stone, M. (2003). Item specification vs. item banking. Rasch Measurement Transactions, 17(3), 929-30 [http://www.rasch.org/rmt/rmt173a.htm].

Turner, J. (1955, November). Maxwell on the method of physical analogy. British Journal for the Philosophy of Science, 6, 226-238.

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