Question: Suppose that there are two examinees: A and B. Both have a score of 25 out of 50 on an ability test. But A answered the 25 most difficult items correctly, and B answered 25 easiest correctly. Is it logical that they have the same Rasch ability estimates? Does a right answer to a hard item more than cancel out a wrong answer to an easy item?
Reply: This isn't merely a "Rasch" problem, but a fundamental conceptual problem in understanding person performance. What is the ability of examinee A, regardless of the analytical model? On the easy items, very incompetent, or very careless, or .... On the hard items, very competent, or very lucky, or ....
If this was a driving test, or a test of surgical skills, we hope examinee A fails. But if this is Albert Einstein on an arithmetic test, we hope he passes.
Under Rasch model conditions, every way of making a raw score has some probability of being observed. It just so happens that A responded in the most unlikely way, and B in the most likely, but, from the Rasch perspective, both manifested the same ability. In effect, the Rasch model takes the position that the penalty for failing an easy item is the same as the credit for succeeding on a hard one, so that all ways of making 25 on 50 items have the same measure. But definitely not the same quality-control fit statistics.
Of course, if you don't believe an examinee's answers to the easy (or hard) items correspond to that examinee's ability, you can make them missing data - if you dare!
The Eternal Question: Is Right worth more than Wrong? Linacre J.M. Rasch Measurement Transactions, 2002, 15:4 p. 855
|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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