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# Statistics and Its Interface

## Volume 5 (2012)

### Number 2

### A modified Bartlett test for linear hypotheses in heteroscedastic one-way ANOVA

Pages: 253 – 262

DOI: http://dx.doi.org/10.4310/SII.2012.v5.n2.a9

#### Authors

#### Abstract

In this paper, we propose and study a so-called modified Bartlett (MB) test for the general linear hypothesis testing (GLHT) problem in heteroscedastic one-way ANOVA. The MB test is easy to compute and implement via using the usual chi-squared distribution. The MB test is shown to be invariant under affine transformations, different choices of the contrast matrix used to define the same hypothesis and different labeling schemes of the population means. Simulation studies demonstrate that the MB test performs well and it outperforms or is comparable to some existing tests for the k-sample Behrens-Fisher problem, a special case of the GLHT problem. The MB test is illustrated using a real data example.

#### Keywords

heteroscedastic one-way ANOVA, general linear hypothesis testing problem, k-sample Behrens-Fisher problem, modified Bartlett correction