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

Formative Use of Intuitive Analysis of Variance

“…As a result, their conceptual reasoning may not develop as readily as their procedural knowledge. Indeed, context, including prior learning experiences, has been identified as having an influence on the development of IIR (see, e.g., Pfannkuch, 2011). Experiment 2, however, provides insight about how appropriately focused, active reflection and analysis of data provided by the intuitive ANOVA task may be used to facilitate development of a deeper understanding of IIR.…”

“…Zieffler, Garfield, delMas, and Reading (2008) described IIR in general as making judgments about populations based on samples using available prior knowledge, but not formal statistical procedures. Pfannkuch (2011), however, argued that while IIR does involve drawing inferences about populations from samples, it goes beyond simply making such conclusions, defining IIR through three additional characteristics: (1) using one's currently developing theoretical knowledge of statistics, rather than formal statistical techniques; (2) considering sampling variability and, therefore, expressing some degree of uncertainty in one's inferences; and (3) seeking and proposing explanations for structure in the data. Likewise, Gil and Ben-Zvi (2011) distinguished informal from formal inferential reasoning by noting that IIR focuses on comparison of distributions of sample data, using conceptual understanding, informal statements of confidence, and explanation, rather than on performing statistical procedures, mathematical calculations, and formal confidence intervals.…”

Model-based Informal Inference

“…6, No. 5;2017 line of best fit shows regarding the relationship amongst these variables in context. They were instructed to run the model repeatedly and draw inferences about the relationship amongst the variables and the line of best fit.…”

“…Informal approaches to statistical inference eschew these formalisms and introduce students to core ideas and techniques in ways that are accessible to learners who are not familiar with formal procedures, thus laying a foundation for their future study of formal statistical inference (Pratt & Ainley, 2008). If informal inferences can provide such a foundation for students' future study of statistics, we must ask questions about how to accomplish this aim in the classroom (Pfannkuch, 2011). My intent hence is to seek literature that aimed for a broad interpretation of modelling that would capture informal statistical inference and the generation of data through activities involving uncertainty.…”

“…These probability distributions that are inherent in statistical models are what distinguish statistical models from other, non-statistical, mathematical models. Whereas, the data-centric perspective moves from data to model/function (Engel & Kuntze;2011, Tukey, 1977. The emphasis is on data, and the modellers begin the modelling process with the study of the data and their distinctive behaviour, (e.g., trend of data, pattern, and variation) in order to build a model or a function.…”