Given sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse these concepts. An excerpt of a national mathematics examination paper, where a sample is mistaken for the population, is used to illustrate this confusion as well as sample variation and its link to sample size. We discuss two techniques that can be used to explain the difference between a parameter and a statistic. The first is a visual technique in which the variability in calculated statistics is contrasted to the fixed value of the corresponding parameter. Thereafter, we discuss Monte Carlo simulation techniques and explain the contribution that these methods may have.
{"title":"The sample is not the population","authors":"J. S. Allison, L. Santana, I. J. H. Visagie","doi":"10.1111/test.12385","DOIUrl":"https://doi.org/10.1111/test.12385","url":null,"abstract":"Given sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse these concepts. An excerpt of a national mathematics examination paper, where a sample is mistaken for the population, is used to illustrate this confusion as well as sample variation and its link to sample size. We discuss two techniques that can be used to explain the difference between a parameter and a statistic. The first is a visual technique in which the variability in calculated statistics is contrasted to the fixed value of the corresponding parameter. Thereafter, we discuss Monte Carlo simulation techniques and explain the contribution that these methods may have.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"61 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Malgorzata Korolkiewicz, Nick Fewster‐Young, Fernando Marmolejo‐Ramos, Florence Gabriel, Pamela Kariuki, Jorge López Puga, Rebecca Marrone, Andrew Miles, Ana María Ruiz‐Ruano García
In an increasingly data‐driven world, statistical literacy is a necessity yet statistical learning is often inhibited by statistics anxiety. Using the Auzmendi Scale to Measure Attitude toward Statistics (ASMAS), this study examines how statistics anxiety in university students is related to other dimensions of their attitudes toward statistics and how statistics anxiety and other dimensions change following introductory statistics instruction. Based on data collected from Spain, Canada, and Australia, this study finds that anxiety is negatively related to security–confidence, pleasantness, and motivation. The structure of these relationships is consistent across countries and disciplines and remains in place after statistics instruction. Further, by the end of an introductory statistics course, students report higher security–confidence and pleasantness but lower anxiety. Results thus suggest where efforts to improve students' experience with statistics might need to be directed, and the paper concludes with a discussion of the implications of these results for statistics instruction.
{"title":"Fear of the unknown: Relationship between statistics anxiety and attitudes toward statistics of university students in three countries","authors":"Malgorzata Korolkiewicz, Nick Fewster‐Young, Fernando Marmolejo‐Ramos, Florence Gabriel, Pamela Kariuki, Jorge López Puga, Rebecca Marrone, Andrew Miles, Ana María Ruiz‐Ruano García","doi":"10.1111/test.12381","DOIUrl":"https://doi.org/10.1111/test.12381","url":null,"abstract":"In an increasingly data‐driven world, statistical literacy is a necessity yet statistical learning is often inhibited by statistics anxiety. Using the Auzmendi Scale to Measure Attitude toward Statistics (ASMAS), this study examines how statistics anxiety in university students is related to other dimensions of their attitudes toward statistics and how statistics anxiety and other dimensions change following introductory statistics instruction. Based on data collected from Spain, Canada, and Australia, this study finds that anxiety is negatively related to security–confidence, pleasantness, and motivation. The structure of these relationships is consistent across countries and disciplines and remains in place after statistics instruction. Further, by the end of an introductory statistics course, students report higher security–confidence and pleasantness but lower anxiety. Results thus suggest where efforts to improve students' experience with statistics might need to be directed, and the paper concludes with a discussion of the implications of these results for statistics instruction.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"198 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joachim Engel, Iddo Gal, Sean McCusker, James Nicholson
{"title":"Tribute to Jim Ridgway and his contributions to statistics education and statistical literacy","authors":"Joachim Engel, Iddo Gal, Sean McCusker, James Nicholson","doi":"10.1111/test.12382","DOIUrl":"https://doi.org/10.1111/test.12382","url":null,"abstract":"","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141883929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jorge N. Tendeiro, Rink Hoekstra, Tsz Keung Wong, Henk A. L. Kiers
Most researchers receive formal training in frequentist statistics during their undergraduate studies. In particular, hypothesis testing is usually rooted on the null hypothesis significance testing paradigm and its p‐value. Null hypothesis Bayesian testing and its so‐called Bayes factor are now becoming increasingly popular. Although the Bayes factor is often introduced as being the Bayesian counterpart to the p‐value, its computation, use, and interpretation are quite distinct from the p‐value. There is now evidence confirming that the application of the Bayes factor in applied research is ill‐devised. To improve the current status quo, we have created a Shiny/R app called the Bayes factor, which offers a dynamic tutorial for learning all the basics about the Bayes factor. In this paper, we explain how the app works and we offer suggestions on how to use it in class or self‐study settings. The app is freely available at https://statsedge.org/shiny/LearnBF/.
大多数研究人员在本科学习期间都接受过频繁统计的正规培训。特别是，假设检验通常植根于零假设显著性检验范式及其 p 值。现在，零假设贝叶斯检验及其所谓的贝叶斯因子正变得越来越流行。尽管贝叶斯因子经常被介绍为 p 值的贝叶斯对应物，但其计算、使用和解释与 p 值截然不同。现在有证据证实，贝叶斯因子在应用研究中的应用并不完善。为了改善目前的现状，我们创建了一个名为贝叶斯因子的 Shiny/R 应用程序，它提供了一个学习贝叶斯因子所有基础知识的动态教程。在本文中，我们将解释该应用程序的工作原理，并就如何在课堂或自学环境中使用该应用程序提出建议。该应用程序可在 https://statsedge.org/shiny/LearnBF/ 免费获取。
{"title":"Introduction to the Bayes factor: A Shiny/R app","authors":"Jorge N. Tendeiro, Rink Hoekstra, Tsz Keung Wong, Henk A. L. Kiers","doi":"10.1111/test.12380","DOIUrl":"https://doi.org/10.1111/test.12380","url":null,"abstract":"Most researchers receive formal training in frequentist statistics during their undergraduate studies. In particular, hypothesis testing is usually rooted on the null hypothesis significance testing paradigm and its <jats:italic>p</jats:italic>‐value. Null hypothesis Bayesian testing and its so‐called Bayes factor are now becoming increasingly popular. Although the Bayes factor is often introduced as being the Bayesian counterpart to the <jats:italic>p</jats:italic>‐value, its computation, use, and interpretation are quite distinct from the <jats:italic>p</jats:italic>‐value. There is now evidence confirming that the application of the Bayes factor in applied research is ill‐devised. To improve the current status quo, we have created a Shiny/R app called <jats:italic>the Bayes factor</jats:italic>, which offers a dynamic tutorial for learning all the basics about the Bayes factor. In this paper, we explain how the app works and we offer suggestions on how to use it in class or self‐study settings. The app is freely available at <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"https://statsedge.org/shiny/LearnBF/\">https://statsedge.org/shiny/LearnBF/</jats:ext-link>.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"66 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peter Holmes, renowned teacher, statistical educator, and founding editor of this journal, passed away peacefully on April 2, 2024, age 86 years. Peter was one of the great UK pioneers of statistical education in the 20th and 21st centuries. He developed a reputation nationally and internationally for his teaching ability, innovative ideas for pedagogy, and resource creation for students and teachers in statistics. Many people benefitted from his skills and generosity of ideas, both in the United Kingdom and globally.
{"title":"Tribute to Peter Holmes and his statistical education achievements","authors":"Neville Davies, Helen MacGillivray","doi":"10.1111/test.12376","DOIUrl":"https://doi.org/10.1111/test.12376","url":null,"abstract":"Peter Holmes, renowned teacher, statistical educator, and founding editor of this journal, passed away peacefully on April 2, 2024, age 86 years. Peter was one of the great UK pioneers of statistical education in the 20th and 21st centuries. He developed a reputation nationally and internationally for his teaching ability, innovative ideas for pedagogy, and resource creation for students and teachers in statistics. Many people benefitted from his skills and generosity of ideas, both in the United Kingdom and globally.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"70 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We explore ways in which statistics can be used to understand disease spread and support decision‐making by governments. “Past performance does not guarantee future results”—we hope. We discuss and show examples from the National Science Foundation (NSF)‐funded COVID‐Inspired Data Science Education through Epidemiology (CIDSEE) project. Throughout, the emphasis is on the relationships between evidence, modeling and theorizing, and appropriate action. Statistics should be an essential element in all these aspects. We point to some “big statistical ideas” that underpin the whole process of modeling, which can be illustrated vividly in the context of pandemics. We argue that statistics education should emphasize the application of statistics in practical situations, and that many curricula do not equip students to use their understandings of statistics outside the classroom. We offer a framework for curriculum analysis and point to some rich teaching resources.
我们探讨如何利用统计数据来了解疾病传播情况，并为政府决策提供支持。我们希望 "过去的表现并不能保证未来的结果"。我们讨论并展示了美国国家科学基金会（NSF）资助的 COVID-Inspired Data Science Education through Epidemiology (CIDSEE) 项目中的实例。我们始终强调证据、建模和理论化与适当行动之间的关系。统计应该是所有这些方面的基本要素。我们指出了一些 "大统计思想"，它们是整个建模过程的基础，可以在大流行病的背景下生动地加以说明。我们认为，统计教育应强调统计在实际情况中的应用，而许多课程并没有使学生具备在课堂之外运用他们对统计的理解的能力。我们提供了一个课程分析框架，并指出了一些丰富的教学资源。
{"title":"New viruses are inevitable; pandemics are optional—Lessons for and from statistics","authors":"James Nicholson, Jim Ridgway","doi":"10.1111/test.12379","DOIUrl":"https://doi.org/10.1111/test.12379","url":null,"abstract":"We explore ways in which statistics can be used to understand disease spread and support decision‐making by governments. “Past performance does not guarantee future results”—we hope. We discuss and show examples from the National Science Foundation (NSF)‐funded COVID‐Inspired Data Science Education through Epidemiology (CIDSEE) project. Throughout, the emphasis is on the relationships between evidence, modeling and theorizing, and appropriate action. Statistics should be an essential element in all these aspects. We point to some “big statistical ideas” that underpin the whole process of modeling, which can be illustrated vividly in the context of pandemics. We argue that statistics education should emphasize the application of statistics in practical situations, and that many curricula do not equip students to use their understandings of statistics outside the classroom. We offer a framework for curriculum analysis and point to some rich teaching resources.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"82 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study investigates a range of non‐normative ideas that pre‐service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre‐service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records of task‐based interviews has articulated fundamental facets of sampling variability that have not yet been fully explicated in the literature, especially with middle grade PSTs. With the content expectation of sampling variability for middle grade students as suggested by policy reports in the United States of America, this study is particularly fertile ground for designing curricula that can support middle grade PSTs' development of critical specialized content knowledge on sampling variability.
{"title":"Pre‐service middle school teachers' specialized content knowledge on sampling variability","authors":"Omar Abu‐Ghalyoun, Adnan Al‐Abed","doi":"10.1111/test.12377","DOIUrl":"https://doi.org/10.1111/test.12377","url":null,"abstract":"This study investigates a range of non‐normative ideas that pre‐service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre‐service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records of task‐based interviews has articulated fundamental facets of sampling variability that have not yet been fully explicated in the literature, especially with middle grade PSTs. With the content expectation of sampling variability for middle grade students as suggested by policy reports in the United States of America, this study is particularly fertile ground for designing curricula that can support middle grade PSTs' development of critical specialized content knowledge on sampling variability.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"364 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In statistics classes, the central limit theorem has been demonstrated using simulation‐based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real‐data‐based simulations are here implemented in which the populations are empirical distributions of data selected from Japanese firms. The dataset chosen contains 38 variables familiar to business students, such as sales and assets. The maximum population size of the variables is 2243. One thousand samples with replacement are selected for specific variable–sample size combinations. Hypothesis testing results indicate that the normality hypothesis for the sample mean is rejected for 31 variables at the 0.1% level even with a sample size of 500. It is emphasized that the data for these variables indicate that this should not be a surprise, and emphasize the importance of looking at data.
{"title":"An empirical study on sample size for the central limit theorem using Japanese firm data","authors":"Kosei Fukuda","doi":"10.1111/test.12378","DOIUrl":"https://doi.org/10.1111/test.12378","url":null,"abstract":"In statistics classes, the central limit theorem has been demonstrated using simulation‐based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real‐data‐based simulations are here implemented in which the populations are empirical distributions of data selected from Japanese firms. The dataset chosen contains 38 variables familiar to business students, such as sales and assets. The maximum population size of the variables is 2243. One thousand samples with replacement are selected for specific variable–sample size combinations. Hypothesis testing results indicate that the normality hypothesis for the sample mean is rejected for 31 variables at the 0.1% level even with a sample size of 500. It is emphasized that the data for these variables indicate that this should not be a surprise, and emphasize the importance of looking at data.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"51 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Udi Alter, Carmen Dang, Zachary J. Kunicki, Alyssa Counsell
The biggest difference in statistical training from previous decades is the increased use of software. However, little research examines how software impacts learning statistics. Assessing the value of software to statistical learning demands appropriate, valid, and reliable measures. The present study expands the arsenal of tools by reporting on the psychometric properties of the Value of Software to Statistical Learning (VSSL) scale in an undergraduate student sample. We propose a brief measure with strong psychometric support to assess students' perceived value of software in an educational setting. We provide data from a course using SPSS, given its wide use and popularity in the social sciences. However, the VSSL is adaptable to any statistical software, and we provide instructions for customizing it to suit alternative packages. Recommendations for administering, scoring, and interpreting the VSSL are provided to aid statistics instructors and education researchers understand how software influences students' statistical learning.
{"title":"The VSSL scale: A brief instructor tool for assessing students' perceived value of software to learning statistics","authors":"Udi Alter, Carmen Dang, Zachary J. Kunicki, Alyssa Counsell","doi":"10.1111/test.12374","DOIUrl":"https://doi.org/10.1111/test.12374","url":null,"abstract":"The biggest difference in statistical training from previous decades is the increased use of software. However, little research examines how software impacts learning statistics. Assessing the value of software to statistical learning demands appropriate, valid, and reliable measures. The present study expands the arsenal of tools by reporting on the psychometric properties of the Value of Software to Statistical Learning (VSSL) scale in an undergraduate student sample. We propose a brief measure with strong psychometric support to assess students' perceived value of software in an educational setting. We provide data from a course using SPSS, given its wide use and popularity in the social sciences. However, the VSSL is adaptable to any statistical software, and we provide instructions for customizing it to suit alternative packages. Recommendations for administering, scoring, and interpreting the VSSL are provided to aid statistics instructors and education researchers understand how software influences students' statistical learning.","PeriodicalId":43739,"journal":{"name":"Teaching Statistics","volume":"21 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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