Genetic covariance constitutes the component on which plant/animal selection can be based upon. This work presents two types of tests of significance for genetic covariance: a test statistic that takes into account the genetic and environmental effects and a test statistic that only considers the genetic information. The first type refers to tests based on the mean cross-products ratio, whose distribution is obtained via nonparametric bootstrap resampling and Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based upon an adaptation of Wilks' and Pillai's statistics for evaluating independence of two sets of variables. Real data are used to illustrate the the tests, both being implemented in R.
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