An Optimization Model for Test Assembly To Match Observed-Score Distributions. Research Report 94-7.

An optimization model is presented that allows test assemblers to control the shape of the observed-score distribution on a test for a population with a known ability distribution. An obvious application is for item response theory-based test assembly in programs where observed scores are reported and operational test forms are required to produce the same observed-score distributions as long as the population of examinees remains stable. The model belongs to the class of 0-1 linear programming models and constrains the characteristic function of the test. The model can be solved using the heuristic presented in Luecht and T. M. Hirsch (1992). An empirical example with item parameters from the ACT Assessment Program Mathematics Test illustrates the use of the model.

[1]  F. Lord.  Applications of Item Response Theory To Practical Testing Problems , 1980 .

[2]  F. Samejima.  Weakly parallel tests in latent trait theory with some criticisms of classical test theory , 1977 .

[3]  Ellen Boekkooi-Timminga,et al.  A Cluster-Based Method for Test Construction , 1990 .

[4]  Melvin R. Novick,et al.  Some latent train models and their use in inferring an examinee's ability , 1966 .

[5]  H. Gulliksen.  Theory of mental tests , 1952 .

[6]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[7]  Wim J. van der Linden,et al.  Algorithms for Computerized Test Construction Using Classical Item Parameters , 1989 .

[8]  Ellen Boekkooi-Timminga.  Simultaneous test construction by zero-one programming , 1986 .

[9]  van der Linden,et al.  Optimal design in item response theory : applications to test assembly and item calibration , 1994 .

[10]  Jos J. Adema,et al.  The Construction of Customized Two-Stage Tests. , 1990 .

[11]  Douglas H. Jones,et al.  Polynomial Algorithms for Item Matching , 1992 .

[12]  Richard M. Luecht,et al.  Computerized Test Construction Using an Average Growth Approximation of Target Information Functions. , 1990 .

[13]  F. Lord.  A strong true-score theory, with applications. , 1965, Psychometrika.

[14]  Ronald D. Armstrong,et al.  An automated test development of parallel tests from a seed test , 1992 .

[15]  T. Theunissen.  Binary programming and test design , 1985 .

[16]  Ellen Boekkooi-Timminga,et al.  A Zero-One Programming Approach to Guiliksen's Matched Random Subtests Method , 1988 .

[17]  W. D. Linden,et al.  Achievement test construction using 0-1 linear programming , 1991 .

[18]  Ellen Boekkooi-Timminga.  The Construction of Parallel Tests From IRT-Based Item Banks , 1989 .

[19]  J. Adema.  Methods and Models for the Construction of Weakly Parallel Tests , 1992 .