Multivariate investigation of Nobel Prize and mathematics education data

This thesis investigates advanced multivariate statistical methods to explore the complex associations between multiple variables relating to mathematics performance of students in high schools in Saudi Arabia. This research is important given recent attention on the performance in mathematics of students in Saudi Arabia, together with the focus on improving education standards in a country with one of the strongest economies internationally. Correspondence analysis is explored to more closely examine the association between multiple categorical variables simultaneously and to establish a framework for use in educational research. A case study is explored to present the logical sequence of steps that form the progression from simple, to multiple and then the more rarely used form in practice, yet the most relevant for our present study, multiway correspondence analysis, to provide valuable insights into the complex nature of the multivariate associations. Insights from the multiway correspondence analysis guide the development of the theoretical framework for the structural equation model, which is a novel approach to theoretical model development. The structural equation modelling framework was further extended to the multilevel framework to account for the structure of students being nested within classes, providing a more comprehensive understanding of the interplay between variables, while also allowing latent variables pertaining to multidimensional educational constructs to be measured by multiple indicator variables. This framework also enabled the investigation of mediation effects. The multilevel structural equation model in the classical framework is further extended to the Bayesian framework to allow a more informative approach to modelling, building on methodology in the Bayesian structural equation modelling context. This further strengthens findings from the classical modelling framework that did not account for aspects of model uncertainty. This research provides a deeper understanding of mathematics education in Saudi Arabia, which could empower educators and policymakers to devise more efficient strategies in an attempt to elevate student academic performance by customising teaching methods and offering additional support to students dealing with heightened anxiety related to mathematics, while addressing disparities due to gender, school type and parental education levels. By addressing this multifaceted range of factors, the education system can potentially better equip students to surpass global academic standards, while strengthening Saudi Arabia's educational infrastructure.