An investigation of methods for reducing sampling error in certain IRT procedures

Abstract

The sampling errors of maximum likelihood estimates of item response theory parameters are studied in the case when both people and item parameters are estimated simultaneously. A check on the validity of the standard error formulas is carried out. The effect of varying sample size, test length, and the shape of the ability distribution is investigated. Finally, the effect of anchor-test length on the standard error of item parameters is studied numerically for the situation, common in equating studies, when two groups of examinees each take a different test form together with the same anchor test. The results encourage the use of rectangular or bimodal ability distributions, and also the use of very short anchor tests.