Statistical Reasoning

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

The paper shows how error statistical theory can be deployed to grasp the deeper epistemic logic of the peer-review process. The intent is to provide the readers with a novel lens through which to make sense of the practices of academic publishing.

Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of standard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the prospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined

In recent years, there has been a growing focus on central statistical ideas or ‘big ideas’ in statistical reasoning such as center, distribution, and variability in research studies. To date, however, there is a paucity of assessments that integrate three statistical reasoning using information technology, i.e. reasoning about center, spread, and distribution for high school students. Thus, a statistical reasoning assessment instrument concerning these domains is developed in order to enhance tenth-grade students’ statistical reasoning abilities during the instruction. Its content was validated by three experts in related fields. There are five statistical reasoning tasks in the assessment instrument which have been created based on the initial statistical reasoning framework. Each item is associated with the sub-processes of four key constructs, i.e. describing data, organizing and reducing data, representing data, and analyzing and interpreting data. The dynamic spreadsheet of GeoGebra software is used as a technological tool in solving tasks. This statistical reasoning assessment instrument can be utilized by instructors and researchers for further investigation in future studies.

Rapan, K., & Valerjev, P. (2020). Test statističkog rasuđivanja [Statistical reasoning test]. In V. Ćubela Adorić (Ed.), Zbirka psihologijskih skala i upitnika - Svezak 10 (pp. 103-112). University of Zadar. U radu je prikazan i opisan test statističkog rasuđivanja kojeg su razvili autori. Opisana su psihometrijska svojstva testa kao i relacije s mjerama drugih konstrukata. Raspravljan je i teorijska osnova testa, kao i njegaova uloga u istraživanjima zadataka mišljenja. Konačno, priložen je i test s uputama za njegovo korištenje. This paper presents the Statistal Reasoning Test which has been developed by the authors. The paper describes psychometrical properties of the test, as well as its relations with other constructs. A copy of the Statistical Reasoning Test (in Croatian) with manual is attached in the appendix.

Recent research in statistical reasoning has focused on the developmental process in students when learning statistical reasoning skills. This study investigates statistical reasoning from the perspective of individual differences. As manifestation of heterogeneity, students’ prior attitudes toward statistics, measured by the extended Survey of Attitudes Toward Statistics (SATS), are used (Schau, Stevens, Dauphinee & DeVecchio, 1995). Students’ statistical reasoning abilities are identified by the Statistical Reasoning Assessment (SRA) instrument (Garfield 1996, 1998a, 2003). The aim of the study is to investigate the relationship between attitudes and reasoning abilities by estimating a full structural equation model. Instructional implications of the model for the teaching of statistical reasoning are discussed.

ABSTRACT. We report a study where 195 students aged 12 to 15 years were presented with computerbased tasks that require reasoning with multivariate data, together with paper-based tasks from a well established scale of statistical literacy. The computer tasks were cognitively more complex, but were only slightly more difficult than paper tasks. All the tasks fitted well onto a single Rasch scale. Implications for the curriculum, and public presentations of data are discussed.

The focus of assessment in statistics has gradually shifted from traditional assessment towards alternative assessment where more attention has been paid to the core statistical concepts such as center, variability, and distribution. In spite of this, there are comparatively few assessments that combine the significant three types of statistical reasoning (reasoning about center, spread, and distribution) with information technology in the context of secondary school students. Hence, this paper intends to discuss the development and initial validation of a technology-based statistical reasoning assessment tool that has been created based on a previously developed statistical reasoning framework. This framework has been useful in evaluating students’ statistical reasoning levels in task-based interviews. The assessment tool formulated through this study will be used to refine and validate the initial statistical reasoning framework. There are five tasks in this instrument and each it...

Until recently, studies within the dual-process approach were mainly focused on group differences in processing, and individual differences were neglected. However, individual differences have proven to be a significant factor in conflict detection efficiency and the overall success in base-rate neglect and similar tasks. This should be taken into consideration within the framework of the Hybrid Model of Dual Processing. New tendencies in the development of this model have focused attention on the degree of mindware instantiation as a predictor of base-rate neglect task efficiency. This study aimed to examine the relationship between mindware and base-rate neglect task efficiency and to test and explore the relationship between base-rate response frequency and conflict detection efficiency and the degree of mindware instantiation. All participants solved base-rate neglect tasks, made judgments of confidence in their responses, and solved the Statistical Reasoning Test, Cognitive Reflection Test and Numeracy Scale. We used the Statistical Reasoning Test as a measure of mindware instantiation. The degree of mindware instantiation was found to be the only significant predictor of base-rate neglect task efficiency and the results showed that participants with a higher degree of mindware instantiation generally made more base-rate responses. No correlation was found between the degree of mindware instantiation and conflict detection efficiency. These findings support the hypothesis that the power of logical intuition depends on the individual's degree of mindware instantiation. Therefore, the results of this research indicate the importance of further research into the role of statistical reasoning in base-rate neglect task efficiency. However, we discuss that there are some methodological limitations in this research which might explain why the degree of mindware instantiation had no relationship with conflict efficiency.

Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of standard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the prospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined.

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Appearing in Proceedings of JSM2018 (Vancouver, BC): Based on a presentation I gave in a session on quantitative literacy that I organized for the Meetings.

Statistical literacy is critically underappreciated across scientific disciplines, and is not part of the training in graduate programs even when “statistics” or “statistical methods” are. It is common to teach “introductory statistics” courses to promote engagement with key concepts and methods in the domain, but statistical literacy involves the selection of appropriate methods from among competing plausible alternatives, as well as the correct application of the methods, and then reasoning with those methods and their results. A new, developmental, model of statistical literacy that is specific for the scientific practitioner was outlined by Tractenberg (2017-a), based on prior models of statistical and scientific thinking. In this model, there are nine elements to statistical literacy: 1) Define a problem based on critical literature review; 2) Identify or choose – and justify - the measurement system; 3) Design the collection of data; 4) Pilot, analysis and interpretation; 5) Discern “exploratory”, “planned”, and “unplanned” data analysis; 6) Hypothesis generation based on planned & unplanned analyses; 7) Interpretation of results; 8) Drawing and contextualize conclusions; and 9) Communication. These knowledge, skills, and abilities (KSAs) are important for an individual to execute when they are doing scientific work, but these KSAs must also be developed to a sufficient level to permit an individual to assess and consume research articles and arguments that use data and inferences.

The nine KSAs that comprise statistical literacy for the practicing scientist each require considerably more cognitive capacity than “engagement with key concepts and methods”. The aim of this paper is to discuss the relationship between purposeful development of these KSAs and Bloom’s taxonomy of educational outcomes (cognitive) so that statistical literacy can be clearly seen as a learnable, improvable skill set that can be introduced in the context of a journal club, among other options, and can continue to be used and developed by individuals and instructors.

Evolutionary approaches to judgment under uncertainty have led to new data showing that untutored subject reliably produce judgments that conform to may principles of probability theory when (a) they are asked to compute a frequency instead of the probability of a single event, and (b) the relevant information is expressed as frequencies. But are the frequency-computation systems implicated in these experiments better at operating over some kinds of input than others? Principles of object perception and principles of adaptive design led us to propose the individuation hypothesis: that these systems are designed to produce well-calibrated statistical inferences when they operate over representations of “whole” objects, events, and locations. In a series of experiments on Bayesian reasoning, we show that human performance can be systematically improved or degraded by varying whether a correct solution requires one to compute hit and false-alarm rates over “natural” units, such as whole objects, as opposed to inseparable aspects, views, and other parsings that violate evolved principles of object construal.

To date, there are abundant studies on statistical reasoning in descriptive statistics and inferential statistics. Nevertheless, the types of statistical reasoning assessments used in those studies are different from each other. Hence, this qualitative meta-analysis is aimed to explore the methods utilized in assessing statistical reasoning among students from all levels in descriptive statistics. A total of 36 studies on reasoning about measures of central tendency, variability and distribution were found and reviewed in this paper. It was noticed that six major types of methods were employed to assess students’ statistical reasoning in descriptive statistics, namely interview, survey or questionnaire, tasks, tests, minute paper, and teaching. This study contributes considerably to the statistical reasoning area as it provides new information on statistical reasoning in descriptive statistics. For future studies, some recommendations are proposed to improve statistical reasoning as...

The idea that naturally sampled frequencies facilitate performance in statistical reasoning tasks because they are a cognitively privileged representational format has been challenged by findings that similarly structured numbers presented as “chances” similarly facilitate performance, based on the claim that these are technically single-event probabilities. A crucial opinion, however, is that of the research participants, who possibly interpret chances as de facto frequencies. A series of experiments here indicate that not only is performance improved by clearly presented natural frequencies rather than chances phrasing, but also that participants who interpreted chances as frequencies rather than probabilities were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.

The study reports on collaborations with practitioners to examine the results of students’ performances on high stakes tests as a means to strengthen practitioners’ knowledge of probability and statistics and to empower their conduct of investigations on student performance. Four issues are summarized: the development of their statistical reasoning, their understanding of the meaning of and relationships among the concepts of validity, reliability and fairness as applied to testing, their introduction to the history of testing and its relationship to science, society and cultural inequality, and their reports of independent inquiries. Data on performance on pre- and post-tests demonstrate growth in teacher reasoning and in their professionalism in raising important issues about testing.

The study reports on collaborations with practitioners to examine the results of students’ performances on high stakes tests as a means to strengthen practitioners’ knowledge of probability and statistics and to empower their conduct of investigations on student performance. Four issues are summarized: the development of their statistical reasoning, their understanding of the meaning of and relationships among the concepts of validity, reliability and fairness as applied to testing, their introduction to the history of testing and its relationship to science, society and cultural inequality, and their reports of independent inquiries. Data on performance on pre- and post-tests demonstrate growth in teacher reasoning and in their professionalism in raising important issues about testing.

The focus of assessment in statistics has gradually shifted from traditional assessment towards alternative assessment where more attention has been paid to the core statistical concepts such as center, variability, and distribution. In spite of this, there are comparatively few assessments that combine the significant three types of statistical reasoning (reasoning about center, spread, and distribution) with information technology in the context of secondary school students. Hence, this paper intends to discuss the development and initial validation of a technology-based statistical reasoning assessment tool that has been created based on a previously developed statistical reasoning framework. This framework has been useful in evaluating students’ statistical reasoning levels in task-based interviews. The assessment tool formulated through this study will be used to refine and validate the initial statistical reasoning framework. There are five tasks in this instrument and each it...

Statistical reasoning should precede the statistical  method in the teaching of statistics because the students should master the concepts before they perform computations. To find out whether the students were aware of this principle, the present study explored their preference and the underlying reasons. Twenty undergraduates were taught central tendency and variability by using statistical method (with machine computation) and statistical reasoning (with manual computation) respectively in one session. Most of them turned out to prefer to reason and compute numeric data manually because they understood the statistical concepts and the process of the computation. On the other hand, the rest of the undergraduates preferred the teaching of statistics using the statistical method with machine computation for three reasons: accuracy, efficiency, and convenience. The implications of these findings for the teaching of statistics were presented.

Based on a synthesis of literature, earlier studies, analyses and observations on high school students, this study developed an initial framework for assessing students' statistical reasoning about descriptive statistics. Framework descriptors were established across five levels of statistical reasoning and four key constructs. The former consisted of idiosyncratic reasoning, verbal reasoning, transitional reasoning, procedural reasoning, and integrated process reasoning. The latter include describing data, organizing and reducing data, representing data, and analyzing and interpreting data. In contrast to earlier studies, this initial framework formulated a complete and coherent statistical reasoning framework. A statistical reasoning assessment tool was then constructed from this initial framework. The tool was administered to 10 tenth-grade students in a task-based interview. The initial framework was refined, and the statistical reasoning assessment tool was revised. The ten...