The randomization model for experiments in block designs and the recovery of inter-block information

A general randomization model for experiments in block designs and conditions for obtaining the best linear unbiased estimators of treatment parametric functions under the model are re-examined. It is shown how the best linear unbiased estimators under the overall randomization model can be obtained when the variance components are known. Furthermore, a general method of estimating these, usually unknown, variance components is described and properties of the resulting estimators of treatment parametric functions are considered. In connection with this the recovery of inter-block information in a general block design is discussed.