In large-scale assessments, such as state-wide testing programs, national sample-based assessments, and international comparative studies, there are many steps involved in the measurement and reporting of student achievement. There are always sources of inaccuracies in each of the steps. It is of interest to identify the source and magnitude of…

The discussion here covers five articles that are linked in the sense that they all treat population invariance. This discussion of population invariance is a somewhat broader treatment of the subject than simply a discussion of these five articles. In particular, occasional reference is made to publications other than those in this issue. The…

This article discusses the five studies included in this issue. Each article addressed the same topic, population invariance of equating. They all used data from major standardized testing programs, and they all used essentially the same statistics to evaluate their results, namely, the root mean square difference and root expected mean square…