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.
Funding Statement
Wang’s and Wen’s research was sponsored by the Ministry of Science and Technology, Taiwan (MOST 109-2118-M-006-004-MY2). The research of Zhong was supported by the Ministry of Educational of China project of Humanities and Social Sciences (21YJC910011), the Education and Scientific Research Foundation for Young Scholars in Fujian Province, China (JAT190665).
Citation
Wei-Ming Wang. Chun-Che Wen. Tsai-Hsiang Hung. Junjiang Zhong. Miin-Jye Wen. "Single-stage sampling procedure for heteroscedasticity analysis of means." Braz. J. Probab. Stat. 36 (4) 704 - 724, December 2022. https://doi.org/10.1214/22-BJPS550
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