Sufficient statistic and estimates of covariance special structure matrices in two models of experimental design

For an experiment planning model with random blocks, sufficient statistic, their distributions and unbiased estimates of covariance matrices belonging to the commutator algebra of a model symmetry group are found. For latin squares the relation between commutator algebra and relationship algebra by A. T. James, sufficient statistical data, their distribution and unbiased estimates of covariational matrices are found.