Agrupamento de MÃdias via Bootstrap para populaÃÃes normais e nÃo normais / Grouping means via bootstrap for normal and non-normal populations

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

Multiple comparison procedures are used to compare factor levels means. Nevertheless the most popular tests show problems concerning the ambiguity of results and the control of type I error, some of which were considered conservative and other liberal. Methods based on cluster analysis have been proposed to avoid ambiguity. The present work aims to propose a bootstrap alternative to one of Caliński &Corsten (1985) multiple comparison procedures based on cluster analysis and evaluate the original and bootstrap tests by Monte Carlo simulation considering normal and non-normal probabilistic models. The methodology by Caliński &Corsten (1985) uses the extension of a simultaneous test based on studentized range. N=1000 simulations of k unstructured and qualitative populations were considered. In each simulation r sample sizes (4, 10 e 20) of each of the k populations (5, 10, 20 e 80) (factor levels) were generated. The probabilistic models exponencial, lognormal and normal were considered for the populations. Under complete H0 there were no factor effects. Thus the factorÂs levels presented common mean and common variance. Under partial H0 situation it was considered two groups for which the procedure used for H0 complete is applied. The densities between the groups had different values for the parameters. Under H1 the densities were considered all different. In the normal case they differentiate themselves only for the mean Â, maintaining variance σ2 constant. The two methods were applied in all the simulated configurations. In the N experiments generated from each one of them the performance was evaluated in relation to the type I error rates per experiment (under complete and partial H0 situations) and in relation to the power (under partial H0 and H1 situations). The normal distribution situation was used as suitable environment due to the fact that the Caliński &Corsten test was idealized under the assumption of normality. The simulation software was implemented in R. Thus, it could be concluded that the two tests are exact under complete H0 and normality; under non-normality and complete H0 the bootstrap test controls the type I error per experiment and it is robust; under non-normality and complete H0 the original test is conservative for small values of k and it is liberal for great values of k; in general, under partial H0 situation, the two tests are liberal for smaller differences between groups and they are conservative for greater differences; the power of bootstrap test is considered higher than the original test under partial H0 and H1; in general, the bootstrap test performance is considered robust and superior to the original test being, therefore, recommended.

ASSUNTO(S)

multiple comparison bootstrap comparaÃÃes mÃltiplas monte carlo estatistica monte carlo bootstrap

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