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Plug‐in tests for nonequivalence of means of independent normal populations
Author(s) -
Choi Sungwoo,
Park Junyong
Publication year - 2014
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201300182
Subject(s) - statistics , homogeneity (statistics) , null hypothesis , mathematics , variance (accounting) , range (aeronautics) , analysis of variance , f test of equality of variances , statistical hypothesis testing , population , test statistic , engineering , demography , accounting , sociology , business , aerospace engineering
In this paper, we consider the problem of testing nonequivalence of several independent normal population means. It is a well‐known problem to test the equality of several means using the analysis of variance (ANOVA). Instead of determining the equality, one may consider more flexible homogeneity, which allows a predetermined level of difference. This problem is known as testing nonequivalence of populations. We propose the plug‐in statistics for two different measures of variability: the sum of the absolute deviations and the maximum of the absolute deviations. For each test, the least favorable configuration (LFC) to ensure the maximum rejection probability under the null hypothesis is investigated. Furthermore, we demonstrate the numerical studies based on both simulation and real data to evaluate the plug‐in tests and compare these with the range test.