This study focused on the incidence, correlates, and effects of mathematics anxiety among Japanese children. A translation of the Mathematics Anxiety Rating Scale for Elementary School Students (MARS-E) was completed by 154 fifth- and sixth-grade students. Factor analysis identified four dimensions of math anxiety, and factor scores were computed. Measures of correlation revealed a number of significant relationships between MARS-E scores and classroom achievement grades, gender, and class. Comparison of mean factor scores for each dimension and the three independent variables revealed significant differences among low, middle, and high achievers. Findings are compared with those of a study of American children, and methodological issues are discussed.
While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian methods should be included in classes that cover the P value and Hypothesis Testing. We discuss several fallacies associated with the P value and Hypothesis Testing, including why Fisher's P value and Neyman-Pearson's Hypothesis Tests are incompatible with each other and cannot be combined to answer the question "What is the probability of the truth of one's belief based on the evidence?" We go on to explain how the Minimum Bayes Factor can be used as an alternative to frequentist methods, and why the Bayesian approach results in more accurate, credible, and relevant test results when measuring the strength of the evidence. We conclude that educators must realize the importance of teaching the correct interpretation of Fisher's P value and its alternative, the Bayesian approach, to students in an introductory statistics course.
This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities-especially the ones that involve Bayes' rule -with the help of such traditional approaches as formula use or conversion to natural frequencies. The truth table approach is an alternative method for explaining the concept and calculation procedure of conditional probability and Bayes' rule.
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.
This study explores the potential utility of Bayesian statistical method in determining the predictability of multiple polls—it compares Bayesian technique to the classical statistical method employed by pollsters.
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