LINKING ERRORS IN TREND ESTIMATION IN LARGE‐SCALE SURVEYS: A CASE STUDY

Abstract

ABSTRACTOne of the major objectives of large‐scale educational surveys is reporting trends in academic achievement. For this purpose, a substantial number of items are carried from one assessment cycle to the next. The linking process that places academic abilities measured in different assessments on a common scale is usually based on a concurrent calibration of adjacent assessments using item response theory (IRT) models. It can be conjectured that the selection of common items has a direct effect on the estimation error of academic abilities due to item misfit, small changes in the common items, position effect, and other sources of constructirrelevant changes between measurement occasions. Hence, the error due to the common‐item sampling could be a major source of error for the ability estimates. In operational analyses, generally two sources of error are accounted for in variance estimation: student sampling error and measurement error. A double jackknifing procedure is proposed to include a third source of the estimation error, the error due to common‐item sampling. Three different versions of the double jackknifing were implemented and compared. The data used in this study were item responses from Grade 4 students who took the NAEP 2004 and 2008 math long‐term trend (LTT) assessments. These student samples used in this study are representative samples of Grade 4 student population in 2004 and in 2008 across the US. The results showed that these three double jackknifing approaches resulted in similar standard error estimates that were slightly higher than the estimates from the traditional approach, regardless of whether an item sampling scheme was used or items were dropped at random.