Achievement tests and optimal design for pretesting of questions

Achievement tests are used to measure the students' proficiency in a particular knowledge. Computerized achievement tests (e.g. GRE and SAT) are usually based on questions available in an item bank to measure the proficiency of students. An item bank is a large collection of items with known characteristics (e.g. difficulty). Item banks are continuously updated and revised with new items in place of obsolete, overexposed or flawed items over time. This thesis is devoted to updating and maintaining the item bank with high-quality questions and better estimations of item parameters (item calibration). The thesis contains four manuscripts. One paper investigates the impact of student ability dimensionality on the estimated parameters and the other three deal with item calibration. In the first paper, we investigate how the ability dimensionality influences the estimates of the item-parameters. By a case and simulation study, we found that a multidimensional model better discriminates among the students. The second paper describes a method for optimal item calibration by efficiently selecting the examinees based on their ability levels. We develop an algorithm which selects intervals for the students' ability levels for optimal calibration of the items. We also develop an equivalence theorem for item calibration to verify the optimal design. The algorithm developed in Paper II becomes complicated with the increase of number of calibrated items. So, in Paper III we develop a new exchange algorithm based on the equivalence theorem developed in Paper II. Finally, the fourth paper generalizes the exchange algorithm described in Paper III by assuming that the students have multidimensional abilities to answer the questions.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.