Applets to Support Reasoning about Explained and Unexplained Variability

Reasoning about overall variability in a data set, and the partitioning of variability into explained and unexplained, is a key aspect of statistical reasoning. It also provides a powerful conceptual framework for unifying several sometimes disparate topics of introductory statistics such as linear regression, ANOVA, and significance testing of a fitted model. This type of reasoning creates a platform for comparing statistical models and hence lays a foundation for inferential thinking. We will describe a pair of applets that have been developed with the explicit aim of helping students to reason visually about the partitioning of variability into explained and unexplained variability. The first applet deals with the case of a numeric explanatory variable (regression for bivariate data), the second with the case of a categorical explanatory variable (single-factor ANOVA). We highlight some aspects of the applets’ design which are of pedagogical relevance, and discuss how the applets may support possible learning trajectories for reasoning about variability in the topics of regression, ANOVA and statistical modelling.