Abstract
The present work emphasizes the importance of testing hypothesis on homogeneity of covariance matrices from multivariate k populations. The violation of the assumption of the homogeneity of covariance matrices affects the performance of the tests and the coverage probability of the confidence regions. This work intends to apply two tests of homogeneity of covariance and to evaluate type I error rates and power using Monte Carlo simulation in normal populations and robustness in non normal populations. Multivariate Bartlett's test (MBT) and its bootstrap version (MBTB) were used. Different configurations are tested combining sample sizes, number of variates, correlation and number of populations. Results show that the bootstrap test was considered superior to the asymptotic test and robust, since it controls the type error I rate.
Highlights
IntroductionIn general, is assumed normality, homogeneity of the covariance matrices and independence of the sample observations
In the multivariate inference, in general, is assumed normality, homogeneity of the covariance matrices and independence of the sample observations
The type I error is committed when ones rejects the null hypothesis given that it is true and the probability of incurring in this type error is given by the significance level (MOOD et al, 1974)
Summary
In general, is assumed normality, homogeneity of the covariance matrices and independence of the sample observations. The violation of the assumption of covariance homogeneity has directly effects on tests performance and on the coverage probability of the confidence regions For this reason tests for the null hypothesis of equality of k populational covariance matrices must be applied. When testing the hypotheses the researcher takes the risk of making wrong decisions, in other words, to incur in errors. These are called type I and type II errors. For any tests of hypotheses or decision rules have acceptable results, they should be planed to minimize the decision errors This is not a simple task, because for a settled sample size, the attempt to reduce certain type of error is accompanied by the increment of the other. A balance among these error rates is essential, so that the type II error rate is not excessively
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