Assessment of Informal Statistical Inference

Abstract

In recent studies in statistics education, the teaching and learning of informal statistical inference have been emphasized as a precedence stage of formal statistical inference, which is taught at the tertiary level. Subsequently, there is an abundance of research identifying the meaning of informal statistical inference and exploring ways of improving students informal statistical inference abilities. As research on how to instruct informal statistical inference grows, how to assess students informal statistical inference abilities should be discussed. There has been a need for assessment methods that reflect and align with the characteristics of statistics, but substantive discussion about such assessments are still lacking. Thus, this study aims to clarify the nature of informal statistical inference and to propose appropriate assessment methods that reflect its nature. Through an epistemological analysis of statistical inference, it is found that a statistical inference consists of two thinking components, abduction and induction. Statistical inference as induction can regulate its inherent characteristic according to how it deals with the uncertainty. To address the dilemmas posed by uncertainty, statistical inference uses the quantification of uncertainty using probability and applies modus tollens. Statistical inference as abduction is introduced to denote the importance of generating the simplest and most likely explanation of a hypothesis based on the characteristics and patterns of the sample and the context. Both induction and abduction serve as components of thinking in regard to statistical inference and need to be recognized as separate stages. Through a didactical review of research on informal statistical inference, the treatment of essential concepts and thinking in informal statistical inference were examined. The essential concepts include descriptive statistics as expectation and variation, sample and population, the size of a sample, and sampling distribution, and the essential thinking includes abduction and induction. In informal statistical inference, abduction and induction are carried out as construction of argumentation and verification of argumentation, respectively. In particular, to address the uncertainty in verification of argumentation, students can use probabilistic representations, draw a conclusion by recognizing the importance of repeated sampling, and attempt to validate the argumentation by establishing norms for dealing with uncertainty during the communication. The characteristics of informal statistical inference include that it is an informal argumentation using natural language, that it is based on context, and that it occurs within an interaction. Therefore, the realization of informal statistical inference demands a situation of teaching and learning processes in which communication occurs based on argumentation using verbal language. Due to the nature of informal statistical inference, assessments must occur in parallel with the teaching and learning process. For this reason, the meaning of integration of instruction and assessment was examined and several assessment models, such as the general assessment triangle model and assessment models based on interaction, were analyzed. As a result, an assessment model for informal statistical inference was developed. The assessment model includes the integration of instruction and assessment as a universal set and interaction between a teacher and students as two intersecting sets. The procedure of assessment is represented in the intersection, which consists of a teachers providing tasks, students initial responses, a teachers interpretation based on an assessment element, a teachers feedback, and students final responses. The characteristics of proper assessment tasks, the assessment elements, and the proper method for providing feedback for assessing informal statistical inference are described. Finally, the pedagogical implication of the study is discussed, and future research based on the assessment model developed in the study is suggested.