An alternative teaching method of conditional probabilities and Bayes' rule: an application of the truth table

Satake, Eiki; Murray, Amy Vashlishan

doi:10.1111/test.12080

Cited by 5 publications

(6 citation statements)

References 16 publications

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“…This comparative assessment could, for example, be applied to teaching Bayesian reasoning. While Bayesian reasoning has typically been taught through a thorough dissection of Bayes' rule, it can also be taught using practical in-class games (Holt & Anderson, 1996), truth tables (Satake & Vashlishan Murray, 2015), mosaic plots (White & Warr, 2021), and frequency trees (Sedlmeier & Gigerenzer, 2001). Comparing student progress for each of these didactic methods could provide us with information as to their relative effectiveness.…”

Section: Gaps and Opportunitiesmentioning

confidence: 99%

Perspectives on Scientific Error

Ravenzwaaij¹,

Bakker²,

Heesen³

et al. 2022

Preprint

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Theoretical arguments and empirical investigations indicate that a high proportion of published findings are false or do not replicate. The current position paper provides a broad perspective on this scientific error, focusing both on reform history and on opportunities for future reform. Talking points are organised along four main themes: methodological reform, statistical reform, publishing reform, and institutional reform. For each of these four themes, we discuss the current state of affairs, existing knowledge gaps, and opportunities for future reform. The resulting agenda should provide a useful resource for ushering in an era that is marked by a lower prevalence of scientific error.

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Section: Gaps and Opportunitiesmentioning

confidence: 99%

Perspectives on Scientific Error

Ravenzwaaij¹,

Bakker²,

Heesen³

et al. 2022

Preprint

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show abstract

“…Clearly, more work is needed to determine the relative effectiveness of these approaches. In particular, not all proposed representations have been thoroughly compared, including, for example, "truth tables" that enumerates the logical relationships between hypotheses and observations (Satake & Vashlishan Murray, 2015).…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Strategies for Using a Spatial Method to Promote Active Learning of Probability Concepts

Starns

Cohen

Vargas

et al. 2021

Journal of Statistics and Data Science Education

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We developed and tested strategies for using spatial representations to help students understand core probability concepts, including the multiplication rule for computing a joint probability from a marginal and conditional probability, interpreting an odds value as the ratio of two probabilities, and Bayesian inference. The general goal of these strategies is to promote active learning by introducing concepts in an intuitive spatial format and then encouraging students to try to discover the explicit equations associated with the spatial representations. We assessed the viability of the proposed active-learning approach with two exercises that tested undergraduates' ability to specify mathematical equations after learning to use the spatial solution method. A majority of students succeed in independently discovering fundamental mathematical concepts underlying probabilistic reasoning. For example, in the second exercise, 76% of students correctly multiplied marginal and conditional probabilities to find joint probabilities, 86% correctly divided joint probabilities to get an odds value, and 69% did both to achieve full Bayesian inference. Thus, we conclude that the spatial method is an effective way to promote active learning of probability equations.

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“…The quiz was designed to demonstrate the applicability of Bayes' Rule to a variety of different contexts (medical, mass communication, and politics) utilizing examples from a range of high quality educational materials focused on Bayesian analysis (Satake, et al 1995;Chase and Bown 2000;Albert and Rossman 2009). The three-item quiz was graded out of three points using a rubric that awarded partial points for setting up the equation correctly and selecting the appropriate numbers to use in the formula for Bayes' Rule.…”

Section: Figure 2 Assessment Of Learningmentioning

confidence: 99%

“…" (p. 61) Research in statistics education suggests a prevailing belief that Bayesian approaches are not necessary for the understanding of subsequent statistical content (Rossman and Short 1995). Further, the use of Bayes' Rule is foreign to most students and instructors at the introductory level (Satake, Gilligan and Amato 1995;Satake and Amato 2008;Maxwell and Satake 2010). With a few notable exceptions, for example (Albert 1993), most of the texts, software packages, and instructors at the introductory and intermediate levels, have, either intentionally or unintentionally, long neglected and avoided Bayesian methods.…”

Section: Introductionmentioning

confidence: 99%

“…Since many students may enter careers that will include a Bayesian approach to research, the importance and practical necessity of integrating Bayes' Rule within the teaching of conditional probability is becoming increasingly clear (Satake and Amato 2008). Although several undergraduate-level textbooks that are written from a Bayesian perspective, and/or that present the clinical application of Bayes' Rule, are currently available (Berry 1996;Albert and Rossman 2009;Agresti and Franklin 2012;Peck, Olsen and Devore 2012), our informal survey of several other widely-used introductory level statistics textbooks indicates that textbooks typically dedicate a single page to Bayesian statistics, suggesting that the topic of Bayes' rule is considered optional at best (De Veaux, Velleman and Bock 2008;Pfenning 2011;Utts and Heckard 2011).…”

Section: Introductionmentioning

confidence: 99%

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Teaching an Application of Bayes' Rule for Legal Decision-Making: Measuring the Strength of Evidence

Satake

Murray

2014

Journal of Statistics Education

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Although Bayesian methodology has become a powerful approach for describing uncertainty, it has largely been avoided in undergraduate statistics education. Here we demonstrate that one can present Bayes' Rule in the classroom through a hypothetical, yet realistic, legal scenario designed to spur the interests of students in introductory-and intermediate-level statistics classes. The teaching scenario described in this paper not only illustrates the practical application of Bayes' Rule to legal decision-making, but also emphasizes the cumulative nature of the Bayesian method in measuring the strength of the evidence. This highlights the Bayesian method as an alternative to the traditional inferential methods, such as p value and hypothesis tests. Within the context of the legal scenario, we also introduce DNA analysis, implement a modified version of Bayes' Rule, and utilize Bayes' Factor in the computation process to further promote students' intellectual curiosities and incite lively discussion pertaining to the jury decision-making process about the defendant's status of guilt.

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An alternative teaching method of conditional probabilities and Bayes' rule: an application of the truth table

Cited by 5 publications

References 16 publications

Perspectives on Scientific Error

Perspectives on Scientific Error

Strategies for Using a Spatial Method to Promote Active Learning of Probability Concepts

Teaching an Application of Bayes' Rule for Legal Decision-Making: Measuring the Strength of Evidence

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