Optimal Test Design for Estimation of Mean Ability Growth

The design of an achievement test is crucial for many reasons. This article focuses on a population's ability growth between school grades. We define design as the allocating of test items concerning the difficulties. The objective is to present an optimal test design method for estimating the mean and percentile ability growth with good precision. We use the asymptotic expression of the variance in terms of the test information. With that criterion for optimization, we propose to use particle swarm optimization to find the optimal design. The results show that the allocation of the item difficulties depends on item discrimination and the magnitude of the ability growth. The optimization function depends on the examinees' abilities, hence, the value of the unknown mean ability growth. Therefore, we will also use an optimum in-average design and conclude that it is robust to uncertainty in the mean ability growth. A test is, in practice, assembled from items stored in an item pool with calibrated item parameters. Hence, we also perform a discrete optimization using simulated annealing and compare the results to the particle swarm optimization.