An optimal test design to evaluate the ability of an examinee by using the stress–strength model
Hideo Hirose · Journal of Statistical Computation and Simulation · 2009
Although the item response theory (IRT) has been widely used to test systems such as the Test of English as a Foreign Language (TOEFL), it is not well known to teachers of mathematics in universities and colleges. The superiority of the IRT over the classical test method is also valid in mathematics in universities and high schools. Since the number of problems in mathematics to be tested in a short time period is strictly limited, particularly in universities, an accurate and efficient method to evaluate the abilities of students is strongly required. In this paper, we propose to use the stress–strength model to estimate the students’ abilities. To perform the optimal test, the up-and-down method by Dixon and Mood [W.J. Dixon and A.M. Mood, A method for obtaining and analyzing sensitivity data, J. Am. Statist. Assoc. 54 (1948), pp. 109–126] is incorporated. Then, the proposed model becomes a generalized test model that includes the stratified adaptive test method by Weiss and the up-and-down method [D.J. Weiss, The stratified adaptive computerized ability test, Research Report 73-3, Psychometric Methods Program, Department of Psychology, University of Minnesota, 1973].