In educational tests, a group of questions related to a shared stimulus is called a testlet (e.g., a reading passage with multiple related questions). Use of testlets is very common in educational tests. Additionally, computerized adaptive testing (CAT) is a mode of testing where the test forms are created in real time tailoring to the test…

Mixed-format tests containing both multiple-choice (MC) items and constructed-response (CR) items are now widely used in many testing programs. Mixed-format tests often are considered to be superior to tests containing only MC items although the use of multiple item formats leads to measurement challenges in the context of equating conducted under…

Testing programs often use multiple test forms of the same test to control item exposure and to ensure test security. Although test forms are constructed to be as similar as possible, they often differ. Test equating techniques are those statistical methods used to adjust scores obtained on different test forms of the same test so that they are…

The equity properties can be used to assess the quality of an equating. The degree to which expected scores conditional on ability are similar between test forms is referred to as first-order equity. Second-order equity is the degree to which conditional standard errors of measurement are similar between test forms after equating. The purpose of…

Small sample equating remains a largely unexplored area of research. This study attempts to fill in some of the research gaps via a large-scale, IRT-based simulation study that evaluates the performance of seven small-sample equating methods under various test characteristic and sampling conditions. The equating methods considered are typically…

There has been a steady increase in the use of mixed-format tests, that is, tests consisting of both multiple-choice items and constructed-response items in both classroom and large-scale assessments. This calls for appropriate equating methods for such tests. As Item Response Theory (IRT) has rapidly become mainstream as the theoretical basis for…