Poder e taxas de erro tipo I de quatro critérios multivariados para o teste de igualdade de efeitos de tratamentos avaliados por meio do método de Monte Carlo

Abstract

In the multivariate analysis of variance, four criteria regarded as chiefexist for testing the hypothesis ofequality oftreatment means vectors with approaches by means of the F distribution namely the, criteria by Wilks, Lawley-Hotelling, Roy and that by Pillai. The present work aimed to evaluate, by means ofsimulation, the power and type I error rates ofthese criteria. The language ofthe SAS system - Statistical Analysis System - was utilized to simulate 2000 experiments in severa! situations and in two steps. In the fírst one, the type I error rates were evaluated. For such a number of combinations were done, by takmg into account the number oftreatments equal to 5,10 and 20, replication number equal to 3 and 5, number of variables equal 2 and 3 and variation coefficient of 5, 10 and 20%, fixed, respectively to variables 1, 2 and 3 and still considering the non-existence of effect of treatments. The second step was proceeded under the same condition ofthe fírst one, excepting the manner ofgenerating the effects of treatments. For the treatments effect vectors might be specifíed, successive differences given in function ofthe standard error ofthe parametric means were specifieg. In both steps, the nominal significance leveis of 1% and 5% were adopted. A total of408,000 experimentswas generated. It follows that correlation structure among the variables did not affect the type I error rates, but had they influences upon the powerofthe four criteria. Pillai, Wilks and Hoteiling^ criteria proved similar among them as to the type I error rates. PillaTs criterium was the most rigorous for having presented type I error rate signifícantly (p < 0.05) inferior to the nominal leveis, besides having shown less power. Hotelling's criterion presented trend, in some circumstances, of possessing type I error rates statistically (p < 0.05) superior to the nominal levei and general trend of possessing greater type I error rates than Wilks1 and Pillai's criteria. Roy's criterion has a high power, but the type I error rate were statistically (p < 0.05) higher than nominal rates (a=l% or 5%) in every situation, making their utüization unfeasible. Wilks' criterion is advised as ideal to the tests ofthe equality hypothesis ofthe effect of the means vector of treatments of the multivariate analysis of variance, for presenting type I error rates equal to the nominal leveis of significance and power superior to Pillai's criterion, although it possesses slightly poorer power than Hotelling's criterion.