"Terminating the test after answering three consecutive items incorrectly is a common practice with individually-administered intelligence tests. Obviously, treating the not reached items as incorrect (which is the typical interpretation - that the examinee would not have answered any of the remaining items correctly) is not a good idea. This practice results in Rasch ability estimates that are biased. On the other hand, if you treat the data as missing, the bias is not as extreme, but it is still there."
Edward W. Wolfe, Michigan State University
Is this bias a serious problem? Ed Wolfe mentions further that he is doing authoritative simulation studies based on real data. But let's imagine a simple scenario. We have a uniform item bank of Rasch-behaving items. Start by administering an item three logits below the examinee. Then advance up the item bank, administering items equally spaced in difficulty. Stop after three consecutive failures. What examinee measures would we expect to obtain for different items spacings?
The Figure shows the results of a simple simulation study according to these criteria. Values close to -4 logits correspond to no correct answers at all. Although the overall bias is negligible, the impact on individual examinees can be huge! Definitely do not use the "3 error" stopping rule with a test containing closely spaced items!
How Much Bias? Wolfe, E.W., Linacre, J.M. Rasch Measurement Transactions, 2000, 14:2 p.750
|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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