Placing Multiple Tests on a Common Scale Using a Post-test Anchor Design: Effects of Item Position and Order on the Stability of Parameter Estimates

When there is an interest in tracking longitudinal trends of student educational achievement using standardized tests, the most common linking approach generally involves the inclusion of a common set of items across adjacent test administrations. However, this approach may not be feasible in the context of high-stakes testing due to undesirable exposure of administered items. In this paper, we propose an alternative design, which allows for the equating of multiple operational tests with no items in common based on the inclusion of common items in an anchor test administered in a post-test condition. We tested this approach using data from the assessment program implemented in Italy by the National Institute for the Educational Evaluation of Instruction and Training for the years 2010–2012, and from a convenience sample of 832 8th grade students. Additionally, we investigated the impact on functioning of common items of varying item position and orders across test forms. Linking of tests was performed using multiple-group Item Response Theory modeling. Results of linking indicated that operational tests showed little variation in difficulty over the years. Investigation of item position and order effects showed that changes in item position closer to the end of the test, as well as the positioning of difficult items at the beginning or in the middle section of a test lead to a significant increase in difficulty of common items. Overall, findings indicate that this approach represents a viable linking design, which can be useful when the inclusion of common items across operational tests is not possible. The impact of differential item functioning of common items on equating error and the ability to detect ability trends is discussed.