HLM in cluster-randomised trials – measuring efficacy across diverse populations of learners

Abstract

We describe the application of Hierarchical Linear Modelling (HLM) in a cluster-randomised study to examine learning algebraic concepts and procedures in an innovative, technology-rich environment in the US. HLM is applied to measure the impact of such treatment on learning and on contextual variables. We provide a detailed description of such methods, methodically analysing nested classroom data with respect to various outcome measures through HLM.

Keywords:

• cluster-randomised trials
• HLM
• algebra and learning
• SimCalc

Notes

1. Download SimCalc curriculum and software at http://www.kaputcenter.umassd.edu/products/software/smwcomp/download/

2. In our models, all individual student level data were centred at the grand mean of all pre-tests vs. the group (class) level. Care should be taken in deciding which form of centring (if any) should be applied, and how to interpret the results. The reason for choosing grand versus group mean centring relates to research design and sample (see Lüdtke et al. 2009; Sloane 2008).