Computerized Adaptive Testing: The Capitalization on Chance Problem

Abstract

This paper describes several simulation studies that examine the effects of capitalization on chance in the selection of items and the ability estimation in CAT, employing the 3-parameter logistic model. In order to generate different estimation errors for the item parameters, the calibration sample size was manipulated (N = 500, 1000 and 2000 subjects) as was the ratio of item bank size to test length (banks of 197 and 788 items, test lengths of 20 and 40 items), both in a CAT and in a random test. Results show that capitalization on chance is particularly serious in CAT, as revealed by the large positive bias found in the small sample calibration conditions. For broad ranges of theta, the overestimation of the precision (asymptotic Se) reaches levels of 40%, something that does not occur with the RMSE (theta). The problem is greater as the item bank size to test length ratio increases. Potential solutions were tested in a second study, where two exposure control methods were incorporated into the item selection algorithm. Some alternative solutions are discussed.