Testes para comparações múltiplas de médias em experimentos com tendência e dependência espacial

Abstract

The variance analysis is used to evaluate the influence of the effects of treatments on an experiment. This approach uses the F test to decide either the equality or not of these effects. Once this test rejects the hypothesis, it becomes necessary to apply the multiple comparisons test in order to verify which treatments differ from each other. However, the application of these mentioned tests above requires the modeled errors to be independents. Thus in experiments whose spatial components occur, it arises the need for tests that assimilates this information on its composition. Thus, this work had the purpose of analysis for experiments with spatial dependence. Initially, the F test of the analysis of variance was presented and evaluated with the incorporation of the spatial information, with this one being carried out by geostatistical techniques. The trend modeling was approached using a covariates analysis methodology. It is indicated relating to each spatial coordinate with tests for the significance of these effects. In order to discern which treatments differ, it was presented proposals for the inclusion of the information for the tests that evaluate the Tukey contrasts, based in the multivariate t distributions and the studendized range distributions, in addition to the Scott-Knott grouping test. The suitability of these tests was evaluated, through simulation, by obtaining the type I error rates which estimated the proportion of experiments that incorrectly rejected the null hypothesis of equality between treatments. In a second stage of this evaluation, performed in simulated experiments under a true alternative hypothesis, it was estimated the power of the proposed tests, with this power being defined by the ratio between the number of correct decisions and the number of decisions made in an experiment. In this simulation process were considered experiments with 8 treatments and 10 repetitions, whose error was obtained in several configurations of spatial dependence. From this analysis, it was observed that the Scott-Knott test presented greater control of the type I error rates than the tests for the Tukey contrasts, being also more powerful than the previous ones, especially in the ability to detect small differences between the means of the treatments. In addition it comes to, when analyzing some examples of simulated and real experiments, the modeling and the tests for the spatial tendency effects has presented appropriated results. Finally, it was verified that the power of the tests for the spatial approach was superior in all scenarios analyzed than the power of the test obtained through the classical approach. With this being said, it was concluded that the incorporation of the spatial information resulted in a greater efficiency to indicate differences between the treatments when they came from experiments with spatial dependence.