Optimal Test Design for Estimation of Mean Ability Growth

• The design of an achievement test is of importance for many reasons. This paper focuses on the mean ability growth of a population from one school grade to another. With test design, we mean how to allocate the test items concerning difficulties. The objective is to estimate the mean ability growth as efficiently as possible. We use the asymptotic expression for the mean ability growth in terms of the test information. With that expression as the criterion for optimization, we use particle swarm optimization to find the optimal design. The optimization function is dependent on the examinees' abilities, and therefore the value of the unknown mean ability growth. Hence, we will also use an optimum in average design. The conclusion is that we should allocate the common items in the middle of the difficulty span, with the two separate test items on different sides. When we decrease the difference in mean ability between the groups, the ranges of the common and test items coincide more.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences (hsv//eng)

Keyword

test design

item response theory

ability growth

particle swarm optimization

optimal design

optimal in average

Statistics

statistik

Publication and Content Type

vet (subject category)

ovr (subject category)