Considerations for correlation analysis using clustered data: working with the teacher education and development study in mathematics (TEDS-M) and other international studies

The Teacher Education and Development Study in Mathematics (TEDS-M) of 2008 focused on how teachers are prepared to teach mathematics in primary and lower-secondary schools in 17 countries. The main results were published in 2012, and the associated public-use database provides a valuable source for secondary analysis of the collected data. The data originate from complex samples and present a hierarchical structure. With future teachers embedded in programs embedded in institutions, various types of cluster effects can be observed. Complex methods, including the use of sampling weights and replication methods for variance estimation, are therefore required for data analysis. This paper focuses on the aspects that need to be considered during any exploration of relationships between variables. Correlation analysis may produce misleading results if attention is not paid to the structure under which the data were collected. We illustrate our points with exemplary analysis of TEDS-M data and propose some guidelines to address the issue.