Bayesian multiple comparisons in homocedastic and heterocedastic normal models. / ComparaÃÃes MÃltiplas Bayesianas em Modelos Normais HomocedÃsticos e HeterocedÃsticos

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

Multiple comparison procedures are used to compare factorâs levels means. Nevertheless, the most popular tests show problems concerning the ambiguity of results and the control of type I error. Methods based on cluster analysis have been proposed to avoid ambiguity, but they present the problem of being valid only under normality. An alternative to avoid this problem is the use of bayesian procedures. This work proposed bayesian alternatives for multiple comparisons, considering the cases of homogeneity and heterogeneity of variances. The methodology used was the a posteriori multivariate t distribution. A number of k chains of averages were generated, using the Monte Carlo method, assuming constant averages, imposing the null hypothesis H0 in the bayesian method. It was done the standardized range of a posteriori, under H0, obtained in a posteriori distribution of the averages, contemplating the possibility of analyzing both the case of heterogeneous variances and the case of homogeneous variances. To describe the final results of the analyses of the proposed methods, it was considered one real example and four simulated examples. In all of them, data from experiments under H0 and H1 were simulated, being the difference between the means of the levels of the factor two standard errors. In both situations, balanced and homocedastics and not-balanced and heterocedastics were considered. To synthesize the results, the posteriori densities of the distribution of standardized range q were initially gotten. To program the inference about the hypothesis H0, the minimum significant difference and the bayesian confidence interval were obtained. It was calculated a posteriori probability P ( Â i >Âiâ) and obtained a new chain with the lower and upper limits of a posteriori interval for each pair of averages, calculating the a posteriori probability of the intervals to be zero. It was obtained the HPD in chains of posteriori distribution of the differences of two averages, using it in the BOA package. The procedures based on the standardized range were higher than the other studied procedures, once they controlled, in the simulated examples, the type I error and detected most of the differences under H1. The bayesian procedures of multiple comparisons were considered successful.

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agronomia agronomia agronomia agronomia

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