## 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 -3.3-2.2-1.10 1.12.23.3 -30-20-10010 2030 -75-50-25025 5075 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 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
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