一种用于教学的概率分布模型拟合的非正式检验方法的开发

IF 2.2 Q3 Social Sciences
Anna-Marie Fergusson, M. Pfannkuch
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引用次数: 3

摘要

摘要对概率分布模型的拟合进行非正式测试在教育上是高中生正式方法的理想先驱。关于如何教授这种非正式方法的研究有限,缺乏可靠的统计标准来得出结论,以及新西兰的评估要求,导致了这项研究。以泊松分布为重点,采用基于任务的在线访谈程序,对10名12年级教师用于非正式测试概率分布模型拟合度的标准进行了调查。研究发现,教师目前使用的标准不可靠,因为他们无法正确评估模型的适合性,特别是没有考虑样本量。然后,教师们使用第一作者开发的交互式拟合优度模拟视觉推理工具(GFVIT)来确定教师们是否对拟合优度有了任何新的理解。在使用GFVIT后,教师们报告说,他们对模型拟合有了更深入的理解,并且该工具允许他们在通过预期分布形状变化的可视化来测试概率分布模型的拟合时考虑样本量。因此,提出了一种新的概率分布拟合的非正式检验方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Development of an Informal Test for the Fit of a Probability Distribution Model for Teaching
Abstract Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this study. Focusing on the Poisson distribution, the criteria used by ten Grade 12 teachers for informally testing the fit of a probability distribution model was investigated using an online task-based interview procedure. It was found that criteria currently used by the teachers were unreliable as they could not correctly assess model fit, in particular, sample size was not taken into account. The teachers then used an interactive goodness of fit simulation-based visual inference tool (GFVIT) developed by the first author to determine if the teachers developed any new understandings about goodness of fit. After using GFVIT teachers reported a deeper understanding of model fit and that the tool had allowed them to take into account sample size when testing the fit of the probability distribution model through the visualization of expected distributional shape variation. Hence, a new informal test for the fit of a probability distribution is proposed.
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来源期刊
Journal of Statistics Education
Journal of Statistics Education EDUCATION, SCIENTIFIC DISCIPLINES-
CiteScore
1.20
自引率
0.00%
发文量
0
审稿时长
12 weeks
期刊介绍: The "Datasets and Stories" department of the Journal of Statistics Education provides a forum for exchanging interesting datasets and discussing ways they can be used effectively in teaching statistics. This section of JSE is described fully in the article "Datasets and Stories: Introduction and Guidelines" by Robin H. Lock and Tim Arnold (1993). The Journal of Statistics Education maintains a Data Archive that contains the datasets described in "Datasets and Stories" articles, as well as additional datasets useful to statistics teachers. Lock and Arnold (1993) describe several criteria that will be considered before datasets are placed in the JSE Data Archive.
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