Take a look at the most discriminating item on your Test. This item operationalizes your best effort at separating your high performers from your low performers. From the perspective of this item, the distance on the latent variable between the high and low performers is greater than it is for any other item in your Test. Wonderful!?
Statistician William Edwards Deming observed this type of optimization in many industrial processes. Here is a composite of some of his examples: Several machine tools were manufacturing the same component. Different operators employed different tactics for maximizing usable output. Consequently, some of those machine tools were set to tighter tolerances than specified, in order to minimize out-of-"official"-tolerance components. Some operators set their machines within "official" tolerance limits, but deliberately made components toward the larger end of the tolerance interval, so that components could be easily remachined smaller if discovered to be out of tolerance. In fact, every manufactured component represented a personal "best effort" by a machine-tool operator. But W. E. Deming perceived that "We are being ruined by our best efforts" (Neave, 1992).
Optimizing each part does not necessarily optimize the whole. For instance, separately optimizing the performance of each member of a basketball team may not optimize team performance. Separately optimizing each component of an audio amplifier may not optimize audio output quality, indeed with some designs may worsen it. Separately optimizing the skills of each musician may not make the orchestra perform better.
The problem with "best efforts" is that they tend to focus on the immediate situation, ignoring the larger context. Those machine operators were given the specifications for the part they were producing, but had no idea how each of their individual approaches impacted the overall quality of the final product. In fact, the highest quality final product was produced by using the widest allowable tolerance range (which was wider than the overly-cautious design engineers originally specified), and setting the machine tool to work in the center of it. This also reduced rejection rates, remachining and improved component interchangeability.
The same is true of Test items. Allowing excessive variation in item discrimination may optimize individual items, but that variation degrades the meaning and utility of the Test as a whole. So how do we know when an optimizing tactic will work? "Only theory can help us figure out what's right and what's wrong" - Deming again. The Rasch model tells us to aim at the center of the discrimination range, and permits us some, but not too much, variation (RMT 14:3, 743).
Neave H.R. (1992) The Deming Dimension. Knoxville, TN: SPC Press.
Item Discrimination, Test Optimization and W. E. Deming Rasch Measurement Transactions, 2005, 18:4 p. 9
|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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