The consideration of the unit structure in inferences from the experiment

Abstract

The statistical model should correctly express the structure of the experiment. This is necessary to guarantee that the variance components which affect the experimental factor effects are identical to the variance components used to judge the significance of these effects, except for the variance attributable to these effects. The usually formulated statistical model ignores the unit structure which results from restrictions to randomization. Consequently, properties implied by randomization are not appropriately taken into account and inferences may turn out biased. A procedure for identifying the effects related to the unit structure and considering them in the statistical model and in inferences from the experiment is suggested. Particularly, an algorithm for the practical derivation of the expected values of mean squares which take into account the experiment structure is proposed.