New insights into the Conditioning and Gain Score approaches in multilevel analysis

We consider the issue of estimating the effect of a treatment variable on student achievement when a pre-test is available, taking into account the hierarchical structure of the data, with students nested into schools. The treatment variable can be either at student level or at school level. This effect can be estimated alternatively by adjusting for the pre-test score, i.e. conditioning, or by using the difference between post-test and pre-test scores, namely the gain score. The performance of the two approaches depends on pre-test reliability and validity of the common trend assumption. We derive approximated analytical results and we compare the two approaches via a simulation study.