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Title: Optimal pretesting of questions for Swedish national tests in school Authors:  Frank Miller - Stockholm University (Sweden) [presenting]
Ellinor Fackle-Fornius - Department of Statistics (Sweden)
Abstract: Questions for future national tests are usually pretested by voluntary pupils who already have participated in their ordinary national test. Instead of allocating the pretest questions randomly to different classes, the 2022 pretesting for mathematics allocates the questions based on the pupils results from their ordinary national test, i.e., based on the ability of each pupil. We will describe the optimal experimental design method which we used to allocate the questions to the pupils in this years pretesting. Item response theory models were used for each question to describe the probability to answer correctly or to receive a certain number of points. The difficulty of a question and other characteristics are supposed to be estimated as precise as possible in the pretesting. Using a simulated annealing algorithm, we determined a D-optimal design for question-allocation and incorporated some specific constraints for this problem. We show that the chosen design is considerably more efficient than the random allocation of questions.