Marking Out Useful Measures

Linear measurement scales always have two arbitrary components: the location of the "zero" point and the size of the unit (implemented as another point on the scale). This gives scientists and practitioners an opportunity to choose values for these components which enhance the usefulness and meaning of their measures.

Ability of Person relative to Item			Probability of Success on Item
Logits	RITs	CLIPS
-3.3 -2.2 -1.1 0 1.1 2.2 3.3	-30 -20 -10 0 10 20 30	-75 -50 -25 0 25 50 75	4% 10% 25% 50% 75% 90% 96%

The effect of choice of these components can be seen in the measurement of temperature. Gabriel D. Fahrenheit (1686-1736) chose his zero, 0, at the temperature at which salt-water melts in order to avoid negative values for commonly encountered temperatures. Fahrenheit chose the length of his unit so that human body temperature would be 100 (nowadays placed at 98.6). Celsius (1701-1744) placed his 0 at the freezing point of water and his 100 at its boiling point. Neither scientist made "the correct" choice, because no such "truth" exists. However, experience suggests that Celsius made more useful, convenient and easily communicated choices.

These choices are available in Rasch measurement. Most Rasch software routinely locates zero at the mean difficulty of the current set of items with units sized in logits, defined by the stochasticity of the local data. Other choices, however, maybe more useful. In order to give the scale unit a readily understandable probabilistic meaning, we can rescale the logit (see Best Test Design, p.191-204). For instance,setting 1 logit = 9.1 RITs (Rasch Units) or 1 logit = 22.7 CLIPs (Centrally Linear Probability Units) gives the equivalences shown in the Table.

Temperature benchmarks are substantive and hence independent of any particular data. For substantive Rasch benchmarks, imagine archetypical performers yielding the highest and lowest reasonable performances in the measurement context. Identify their locations on the measurement construct, either directly by inspection or via a hypothetical administration of the test protocol. Then label the measure corresponding to the lowest performance as 0, and that of the highest performance as 100. The logit distance between these points provides the linear conversion factor. Measures on this scale can then be communicated as representing the percent of achievement of goal status.

Prompted by an IOMC presentation by Carl V. Granger

Granger C.V. (1996) Marking out useful measures. Rasch Measurement Transactions 10:2 p. 497.

Marking out useful measures. Granger C.V. … Rasch Measurement Transactions, 1996, 10:2 p. 497

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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