This study reviewed the theory of estimation/prediction of treatment means, in randomized block designs, emphasizing aspects of interest to plant breeders. Comparisons were made between analyses based on fixed (intrablock) and mixed (with random treatments effects - recovering intergenotypic information) linear models for identifying the determining factors that may affect the classification of genotypes. The mixed model approach, in comparison with the traditional analyses (marginal means and intrablock analysis), in general, leads to: i) more uniformly distributed treatment means; and ii) selection of different genetic treatments when the genetic variance is small relative to the environmental variance, as well as designs being non-orthogonal and unbalanced. In addition, if treatments of distinct reference populations are evaluated in the same experiment, BLUP prediction can lead to different ranking of means, in comparison with the intrablock analysis, even if designs are balanced and orthogonal.
information recovering; block design; BLUP mean; genotypic selection; shrinkage