Towards more Accessible Conceptions of Statistical Inference

Abstract

Summary. There is a compelling case, based on research in statistics education, for first courses in statistical inference to be underpinned by a staged development path. Preferably over a number of years, students should begin working with precursor forms of statistical inference, much earlier than they now do. A side benefit is giving younger students more straightforward and more satisfying ways of answering interesting real world questions. We discuss the issues that are involved in formulating precursor versions of inference and then present some specific and highly visual proposals. These build on novel ways of experiencing sampling variation and have intuitive connections to the standard formal methods of making inferences in first university courses in statistics. Our proposal uses visual comparisons to enable the inferential step to be made without taking the eyes off relevant graphs of the data.This allows the time and conceptual distances between questions, data and conclusions to be minimized, so that the most critical linkages can be made. Our approach was devised for use in high schools but is also relevant to adult education and some introductory tertiary courses.

The Role of Context in Developing Informal Statistical Inferential Reasoning: A Classroom Study

“…Ideas about sample, population, sample size, and sampling variability were experienced but the connection to the new situation was too dissimilar, suggesting the task-context sequence used in this study needed to include new activities that bridged this gap. Furthermore, a rational basis for making a judgement (e.g., rules of thumb or heuristics) needed to be developed for IIR (Wild, Pfannkuch, Regan, & Horton, 2011).…”

Learning to reason from samples

“…Wild, Pfannkuch, Regan & Horton, 2011). Students need authentic, situated, and rich experiences in taking samples and learning how samples do and do not represent the population prior to formal higher studies of statistics.…”

An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference

“…Although students have difficulty with formal statistical inference, many aspects of inference are relevant for everyday use-making predictions, estimating based on available information, and judging the reasonableness of a solution or a claim all involve making inferences-as well as in workplaces (Bakker et al 2008). It has also been acknowledged that informal statistical inference is to be used with nonspecialists such as school children, introductory statistics students, and in workplace settings (Wild et al 2011).…”

“…Makar and Rubin (2009) identified three features that characterize a statistical inference: (1) a statement of generalization beyond the data, (2) use of data as evidence to support this generalization, and (3) the use of probabilistic (non-deterministic) language that expresses some uncertainty about the generalization. These features apply to both formal techniques such as hypothesis testing (e.g., using a t test) or point estimation and students' beginning informal conceptions of statistical inference (Wild et al 2011).…”