Scientific Theories and Empirical Problems

"Science does not, so far as we know, produce theories which are true or even highly probable. Although rare, it sometimes happens that a theory exactly predicts an experimental outcome. When that desirable result is achieved, there is cause for general rejoicing. It is far more common for the predictions deduced from a theory to come close to reproducing the data which constitute a specific problem, but with no exact coincidence of results. ... Empirical problems are frequently solved because, for problem solving purposes, we do not require an exact, but only an approximate, resemblance between theoretical results and experimental ones."
Larry Laudan, Progress and its Problems. Berkeley, CA: University of California Press, 1977, pp. 23, 224

"Essentially, all models are wrong, but some are useful."
Box, G. E. P., and Draper, N. R., (1987), Empirical Model Building and Response Surfaces, John Wiley & Sons, New York, NY.


The Essential Conditions of Measurement

"Measurement appears to require that three conditions be met. The first of these conditions is that one have a working concept of the character to be measured. A psychologist needs a clear notion of what intelligence is before he constructs a test to measure it. Binet, for example, struggled for some years to get an idea of the character he ought to be trying to measure. The crystallization of a clear concept of what one desires to measure is often a critical point in the development of a field of research. In early work, the concept must almost necessarily be vague and nebulous, representing a sort of groping for something that will satisfy a certain purpose. The measurements resulting from such a concept naturally contain an abundance of spurious elements. The cultivation and delimitation of a valid concept of a critical variable is in itself an important contribution to measurement.

"The second necessary condition of measurement is a satisfactory representation of the character to be measured, in the amount that is exhibited by the phenomenon [e.g., student ability]. By a satisfactory representation, we mean one that is perceptible, accurate, and convenient. In some cases, this is equivalent to saying that, for characteristics which are not directly perceptible, an objectifying function or agent [e.g., a test item] must be found.

"This brings us to our third condition for measurement, which is a basis for quantitative comparison. Measurement is essentially a "more-than" or "less- than" type of comparison between a reference point (usually a mark on a scale) and the phenomenon. Measurement in terms of units which are equal, fixed, and standardized, is of course ordinarily to be preferred where it is possible. In the first place, such measurements can be readily recorded and transmitted to others. In the second place, they ordinarily convey more significance to a larger number of people than do unequal units, or values having special significance because of certain unique experiences connected with them. In the third place, they facilitate - in fact they make possible - quantitative science, with its many interrelations, expressed as laws and functions. To utilize units which do not correspond to our number system (in the sense of equal increments) would be to inject hopeless confusion into problems that are at best baffling."

Douglas E. Scates, excerpted from Psychometrika, March 1937, Vol. 2, No.1, p. 27-34.


"G. Rasch's Probabilistic Models.. book represents an attempt to create new paths for scientific behavioral statistics which, till now, have confused groups with individuals... We encourage as many people as possible to obtain and read the book."
from a 1962 review by Sven Rydberg, University of Stockholm, Nordisk Psykologi, 14(7), p.347-8.


RMT 7:3 Quotations and Notations. … Rasch Measurement Transactions, 1993, 7:3 p.312ff.

Please help with Standard Dataset 4: Andrich Rating Scale Model



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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June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
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