Single-stage sampling procedure for heteroscedasticity analysis of means. (English) Zbl 07644490
Summary: 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.
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