There has been a growing awareness among educational researchers of the consequences of using data-analytic models that fail to account for the inherent clustered or hierarchical sampling structure of the data typically obtained. Such clustering poses special analytic problems related to levels of analysis, aggregation bias, heterogeneity of regression and parameter mis-estimation, with important implications for the correct interpretation of effects. This paper compares the results obtained from fitting single-level and multilevel models to two hierarchically structured data sets designed to explain variation in student achievement. Emphasis is given to the crucial importance of fitting models commensurate with the sampling structure of the data to which they are applied.

The results from national studies of student ability are analysed using Item Response Theory (IRT). This theory describes the relationship between the ability of students taking a test and the difficulty of each item on that test. Using the assumption that a test item is a hard item if only the brightest students answer it correctly and that bright students are those students who can answer even the hardest items correctly, IRT is a generalized iterative procedure that can be used to simultaneously estimate both the difficulty of items on a test and the ability of those taking the test. This talk will give an overview of this technique and will demonstrate its use in measuring student ability. In particular the use of IRT models to construct Maths ability scores will be briefly discussed and how the results are communicated to teachers discussed.