Linking Errors between Two Populations and Tests: A Case Study in International Surveys in Education.

This simulation study was prompted by the current increased interest in linking national studies to international large-scale assessments (ILSAs) such as IEA’s TIMSS, IEA’s PIRLS, and OECD’s PISA. Linkage in this scenario is achieved by including items from the international assessments in the national assessments on the premise that the average achievement scores from the latter can be linked to the international metric. In addition to raising issues associated with different testing conditions, administrative procedures, and the like, this approach also poses psychometric challenges. This paper endeavors to shed some light on the effects that can be expected, the linkage errors in particular, by countries using this practice. The ILSA selected for this simulation study was IEA TIMSS 2011, and the three countries used as the national assessment cases were Botswana, Honduras, and Tunisia, all of which participated in TIMSS 2011. The items selected as items common to the simulated national tests and the international test came from the Grade 4 TIMSS 2011 mathematics items that IEA released into the public domain after completion of this assessment. The findings of the current study show that linkage errors seemed to achieve acceptable levels if 30 or more items were used for the linkage, although the errors were still significantly higher compared to the TIMSS’ cutoffs. Comparison of the estimated country averages based on the simulated national surveys and the averages based on the international TIMSS assessment revealed only one instance across the three countries of the estimates approaching parity. Also, the percentages of students in these countries who actually reached the defined benchmarks on the TIMSS achievement scale differed significantly from the results based on TIMSS and the results for the simulated national assessments. As a conclusion, we advise against using groups of released items from international assessments in national assessments in order to link the results of the former to the latter.