Simulation of the Sampling Distribution of the Mean Can Mislead

Watkins, Ann Vreeland; Bargagliotti, Anna E.; Franklin, Christine

doi:10.1080/10691898.2014.11889716

Cited by 18 publications

(29 citation statements)

References 14 publications

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“…Research shows that trying to put it all together at once at the senior secondary or tertiary level is fraught with difficulty (Lipson 2003;Pfaff and Weinberg 2009;Watkins, Bargagliotti, and Franklin 2014). Perhaps starting earlier with some of the basic ideas based on the foundation of variation would provide meaningful building blocks to be put together later.…”

Section: Discussionmentioning

confidence: 99%

“…It was considered too complex for the developmental levels of the students. Recalling the difficulties that older students experience in coming to terms with this relationship (Lipson 2003;Bargagliotti et al 2014;Watkins, Bargagliotti, and Franklin 2014), the intuitions built about basic prediction from samples may be a useful foundation when other issues, such as increasing sample size, are introduced.…”

Section: Discussionmentioning

confidence: 99%

“…Difficulties for students associated with the ideas of sampling, single samples, repeated sampling, and sampling distributions are well known (Lipson 2003;Chance, delMas, and Garfield 2004;Watkins, Bargagliotti, and Franklin 2014). They are observed for teachers as well as students and are not easy to eradicate (e.g., Bargagliotti et al 2014;Franklin et al 2015).…”

Section: Introductionmentioning

confidence: 99%

“…They are observed for teachers as well as students and are not easy to eradicate (e.g., Bargagliotti et al 2014;Franklin et al 2015). Watkins, Bargagliotti, and Franklin (2014) reported difficulties of students in describing the behaviour of increasing numbers of sample statistics in relation to the population statistic, which has the same value as the corresponding statistic of the sampling distribution. Hodgson and Burke (2000) also reported that repeated random sampling led some students to believe that one random sample was not enough to make a statistical inference and multiple samples must be collected.…”

Section: Introductionmentioning

confidence: 99%

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Repeated Random Sampling in Year 5

Watson¹,

English²

2016

Journal of Statistics Education

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As an extension to an activity introducing Year 5 students to the practice of statistics, the software TinkerPlots made it possible to collect repeated random samples from a finite population to informally explore students' capacity to begin reasoning with a distribution of sample statistics. This article provides background for the sampling process and reports on the success of students in making predictions for the population from the collection of simulated samples and in explaining their strategies. The activity provided an application of the numeracy skill of using percentages, the numerical summary of the data, rather than graphing data in the analysis of samples to make decisions on a statistical question. About 70% of students made what were considered at least moderately good predictions of the population percentages for five yes-no questions, and the correlation between predictions and explanations was 0.78.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Repeated Random Sampling in Year 5

Watson¹,

English²

2016

Journal of Statistics Education

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“…However, when trying to address this misconception, we have observed that statistics educators may have a tendency to show many examples of how biased sampling, question wording, question order, and a variety of other possible sampling and measurement issues can impact results in a dramatic way which can potentially lead students to believe that statistics are so sensitive to these issues that it is rare that results can be trusted (disbelief). For a recent example, see Watkins, Bargagliotti, & Franklin (2014) who suggest that over concern about small sample conditions can contribute to student distrust of statistical inference.…”

Section: Anti-statistical Thinking In Traditional Statistics Coursesmentioning

confidence: 99%

Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout the Undergraduate Curriculum

Tintle

Chance

Cobb

et al. 2015

The American Statistician

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Abstract:The use of simulation-based methods for introducing inference is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve students' statistical thinking. This impact comes from simulation-based methods (a) clearly presenting the overarching logic of inference, (b) strengthening ties between statistics and probability/mathematical concepts, (c) encouraging a focus on the entire research process, (d) facilitating student thinking about advanced statistical concepts, (e) allowing more time to explore, do, and talk about real research and messy data, and (f) acting as a firmer foundation on which to build statistical intuition. Thus, we argue that simulation-based inference should be an entry point to an undergraduate statistics program for all students, and that simulation-based inference should be used throughout all undergraduate statistics courses. In order to achieve this goal and fully recognize the benefits of simulation-based inference on the undergraduate statistics program we will need to break free of historical forces tying undergraduate statistics curricula to mathematics, consider radical and innovative new pedagogical approaches in our courses, fully implement assessment-driven content innovations, and embrace computation throughout the curriculum.

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Margin of Error: Connecting Chance to Plausible

Burrill

2023

Advances in Mathematics Education

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Simulation of the Sampling Distribution of the Mean Can Mislead

Cited by 18 publications

References 14 publications

Repeated Random Sampling in Year 5

Repeated Random Sampling in Year 5

Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout the Undergraduate Curriculum

Margin of Error: Connecting Chance to Plausible

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