This paper is from Session 6E: Modeling distributions to connect chance processes, data production, and data distributions

which comes under Topic 6: Innovation and reform in teaching probability within statistics

Model-based informal inference

Presenter

• Richard Lehrer (Vanderbilt University, United States)

Co-authors

• Min-Joung Kim (Vanderbilt University, United States)
• Ryan Seth Jones (Vanderbilt University, United States)

Abstract

Informal inference refers to making decisions informed by conceptions and representations of sampling variability without recourse to theorems governing formal approaches. To support informal inference, grade 6 middle-school students invented and revised models of chance processes they experienced first-hand by generating repeated measures. These processes provided an accessible interpretation of variability as composed of fixed (signal) and random (error) components. Conducting an analysis of variance and then creating random device analogs of these sources informed model building. Students then generated empirical sampling distributions of model parameters to assist model test and revision. Students used these sampling distributions to guide informal inference. We report on the intelligibility of this form of model-based inference as indicated by results of a flexible interview.