Modelling student performance in a tertiary preparatory course

Abstract

[Abstract]: In this dissertation a review of the literature as it applies to the modelling of educational performance data is undertaken. Statistical linear models, including the novel Beta, Tweedie and Tobit regression models, are then applied to the performance data of students who have undertaken a preparatory mathematics course. These models are then critically reviewed and compared with the commonly used standard linear regression model. Issues that arise from the application of statistical linear models to educational performance data are then explored. For example, the effects of non-Normality, which characterizes educational performance data, and the presence of large numbers of students who fail to complete the course (a characteristic of this particular context), are examined and reported. Both of these effects can violate the underlying assumptions of the standard linear regression model. Simulation studies are then used to assess the appropriateness of the linear model when it is applied under the condition of non-Normality and the presence of large numbers of missing observations. Findings from this study indicate that issues relating to model effectiveness are clouded in the educational context by typically large values of the error variance (high noise) and the difficulty in finding suitable performance predictors. Educational models of performance typically lack statistical power, so that in many instances it doesn’t matter what model is applied to the data. Nevertheless, the study highlights many reasons why models alternative to the standard linear regression model should be applied to such data. For example, in situations where the effect is not constant over the entire domain of the explanatory variable, a linear model based upon the beta distribution will be much more appropriate. Similarly, in situations where the performance data contains exact zeros (for example the performance of students who withdraw from the course without providing any measure of achievement) it is more appropriate to use a Tweedie linear model than the standard linear regression model.