The Computation of Equating Errors in International Surveys in Education

Since the IEA's Third International Mathematics and Science Study, one of the major objectives of international surveys in education has been to report trends in achievement. The names of the two current IEA surveys reflect this growing interest: Trends in International Mathematics and Science Study (TIMSS) and Progress in International Reading Literacy Study (PIRLS). Similarly a central concern of the OECD's PISA is with trends in outcomes over time. To facilitate trend analyses these studies link their tests using common item equating in conjunction with item response modelling methods. IEA and PISA policies differ in terms of reporting the error associated with trends. In IEA surveys, the standard errors of the trend estimates do not include the uncertainty associated with the linking step while PISA does include a linking error component in the standard errors of trend estimates. In other words, PISA implicitly acknowledges that trend estimates partly depend on the selected common items, while the IEA's surveys do not recognise this source of error. Failing to recognise the linking error leads to an underestimation of the standard errors and thus increases the Type I error rate, thereby resulting in reporting of significant changes in achievement when in fact these are not significant. The growing interest of policy makers in trend indicators and the impact of the evaluation of educational reforms appear to be incompatible with such underestimation. However, the procedure implemented by PISA raises a few issues about the underlying assumptions for the computation of the equating error. After a brief introduction, this paper will describe the procedure PISA implemented to compute the linking error. The underlying assumptions of this procedure will then be discussed. Finally an alternative method based on replication techniques will be presented, based on a simulation study and then applied to the PISA 2000 data.