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Computerized Adaptive Testing: The Capitalization on Chance Problem

Published online by Cambridge University Press:  10 January 2013

Julio Olea ,
Juan Ramón Barrada ,
Francisco J. Abad ,
Vicente Ponsoda  and
Lara Cuevas
Julio Olea*
Affiliation:
Universidad Autónoma de Madrid (Spain)
Juan Ramón Barrada
Affiliation:
Universidad de Zaragoza (Spain)
Francisco J. Abad
Affiliation:
Universidad Autónoma de Madrid (Spain)
Vicente Ponsoda
Affiliation:
Universidad Autónoma de Madrid (Spain)
Lara Cuevas
Affiliation:
Universidad Complutense de Madrid (Spain)
*
Correspondence concerning this article should be addressed to Julio Olea. Facultad de Psicología, Universidad Autónoma de Madrid. 28049-Madrid (Spain). Phone: +34 914975204. E-mail: [email protected]
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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 θ, the overestimation of the precision (asymptotic Se) reaches levels of 40%, something that does not occur with the RMSE (θ). 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.

Se describen varios estudios de simulación para examinar los efectos de la capitalización del azar en la selección de items y la estimación de rasgo en Tests Adaptativos Informatizados (TAI), empleando el modelo logístico de 3 parámetros. Para generar diferentes errores de estimación de los parámetros de los ítems, se manipuló el tamaño de la muestra de calibración (N = 500, 1000 y 2000 sujetos), así como la ratio entre tamaño del banco y longitud del test (bancos de 197 y 788 ítems, longitudes del test de 20 y 40 ítems), ambos tanto en un TAI como en un test aleatorio. Los resultados muestran que la capitalización del azar es especialmente importante en el TAI, donde se obtuvo un sesgo positivo en las condiciones de escaso tamaño de la muestra. Para rangos amplios de θ, la sobrestimación de la precisión (Se asintótico) alcanza niveles del 40%, algo que no ocurre con los valores de RMSE (θ). El problema es mayor a medida que se incrementa la ratio entre el tamaño del banco de ítems y la longitud del test. Varias soluciones fueron puestas a prueba en un segundo estudio, donde se incorporaron dos métodos para el control de la exposición en los algoritmos de selección de los ítems. Se discuten también algunas soluciones alternativas.

Keywords

computerized adaptive testingcapitalization on chanceitem parameter estimation.tests adaptativos informatizadoscapitalización del azarestimación de los parámetros de los ítems
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 15 , Issue 1 , March 2012 , pp. 424 - 441
Copyright
Copyright © Cambridge University Press 2012

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