Single-stage sampling procedure for heteroscedasticity analysis of means

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Wei-Ming Wang, Chun-Che Wen, Tsai-Hsiang Hung, Junjiang Zhong, M. Wen
{"title":"Single-stage sampling procedure for heteroscedasticity analysis of means","authors":"Wei-Ming Wang, Chun-Che Wen, Tsai-Hsiang Hung, Junjiang Zhong, M. Wen","doi":"10.1214/22-bjps550","DOIUrl":null,"url":null,"abstract":". The analysis of means (ANOM) is a method that can compare the mean of each treatment to the overall mean. According to the graphical result of a statistical data analysis, we can specify which one is different from another. One of the assumptions of the classical ANOM model is that the variances are equal. However, it is not always true for the practice. To solve unknown and unequal population variances, Nelson and Dudewicz (2002) proposed a two-stage sampling procedure. However, additional samples need to be added in the second stage of the two-stage sampling procedure, so it is not practical all the time due to limited time and insufficient budget. Thus, under heteroscedasticity, we applied Chen and Lam’s (1989) single-stage sampling procedure to solve the drawback of the two-stage sampling procedure. In addition, we also provided an illustrative example and critical values for practical uses. In order to make the procedure user-friendly, we built an interface by using R Shiny.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/22-bjps550","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1

Abstract

. The analysis of means (ANOM) is a method that can compare the mean of each treatment to the overall mean. According to the graphical result of a statistical data analysis, we can specify which one is different from another. One of the assumptions of the classical ANOM model is that the variances are equal. However, it is not always true for the practice. To solve unknown and unequal population variances, Nelson and Dudewicz (2002) proposed a two-stage sampling procedure. However, additional samples need to be added in the second stage of the two-stage sampling procedure, so it is not practical all the time due to limited time and insufficient budget. Thus, under heteroscedasticity, we applied Chen and Lam’s (1989) single-stage sampling procedure to solve the drawback of the two-stage sampling procedure. In addition, we also provided an illustrative example and critical values for practical uses. In order to make the procedure user-friendly, we built an interface by using R Shiny.
均值异方差分析的单阶段抽样程序
平均值分析(ANOM)是一种可以将每个治疗的平均值与总体平均值进行比较的方法。根据统计数据分析的图形结果,我们可以指定哪一个不同于另一个。经典ANOM模型的一个假设是方差相等。然而,这种做法并不总是正确的。为了解决未知和不相等的总体方差,Nelson和Dudewicz(2002)提出了一种两阶段抽样程序。然而,在两阶段采样程序的第二阶段需要添加额外的样本,因此由于时间有限和预算不足,这并不总是可行的。因此,在异方差条件下,我们应用Chen和Lam(1989)的单阶段抽样程序来解决两阶段抽样程序的缺点。此外,我们还提供了一个说明性的例子和实际应用的关键价值。为了使程序用户友好,我们使用R Shiny构建了一个界面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信