Comparações múltiplas bayesianas com erro normal assimétrico

Abstract

Conventional multiple comparisons procedures have been widely used to compare the observed treatment means from designed experiments. Normality (symmetry) of the residuals is a routine assumption for these procedures, but it may be unrealistic, doing the inferences made from these tests are not reliable. We relax this assumption by considering that the model errors follow a skew-normal distributions, which includes normality as a special case and provides flexibility in capturing a broad range of non-normal behavior, by simply adding a parameter that controls the degree of asymmetry. Within this context, we propose three new tests in a Bayesian approach. The first, based on multivariate statistics (TG), is used to test the overall hypothesis of equality of several means independent. The other two, based on quadratic forms (TFQ) and the studentized range (TAE) are used for multiple comparisons. We evaluate the performance of all proposed tests by Monte Carlo simulation in different experimental situations, considering different distributions for residuals, number of treatments, number of sample size and credibility levels. In particular, we evaluated the TG test compared the type I error rates under the null hypothesis and the TFQ and TAE tests, the type I error rates for experiment under the full and partial null hypothesis. The performance of the three tests were also evaluated by power rates under partial null hypothesis. The results of the TG test were compared with the F test and the results of the TFQ and TAE test were compared with the Tukey’s test. The TG and TFQ tests showed good performance by controlling the type I error rates in all simulated circumstances and at the same time, showed higher power close to the usual tests compared. However, less satisfactory results occurred with the TAE test, because, although this test is controlled the type I error rates in all simulated circumstances, the same is not proved to be a powerful test. Finally, we present an application of the proposed tests to a real data set on the red clover plant.