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The analysis of means (ANOM) is a method that can compare the mean of each treatment with the overall mean. As one-way ANOVA, the conventional ANOM is not robust under unequal variances. We applied two inference procedures, single-stage and modified single-stage sampling, to solve heteroscedastic analysis of means (HANOM) under unbalanced design. Using proposed weighted average across groups, the influence of the unknown mean and variance are both eliminated. To validate the stability of HANOM under several scenarios of unequal variances and sample sizes, simulation studies of empirical type I error rate are conducted to test the quality of procedures. A real application is provided for illustrating these two procedures clearly. In addition, we build an user-friendly interface to show the results of the HANOM by using Shiny package in R software. [ABSTRACT FROM AUTHOR]

Given k (≥2) independent and normally distributed populations with unknown means and unknown (and possibly unequal) variances, we used the single-stage sampling procedure for multiple comparison with a control to the problem of unequal sample sizes. A simulation of the family-wise error type I was conducted to validate the quality of the procedure and a numerical example was provided for illustrating this procedure. We provided a user-friendly interface by R shiny to obtain the critical values for the practitioners. [ABSTRACT FROM AUTHOR]