A POPULATION APPROACH TO ANALYSIS OF VARIANCE MODELS

Several authors have contributed to what can now be considered a rathe r complete theory for analysis of variance in cases with orthogonal fa ctors. By using this theory on an assumed basic reference population, the orthogonality concept gives a natural definition of independence b etween factors in the population. By looking upon the treated units in designed experiments as a formal sample from a future population abou t which we want to make inference, a natural parametrization of expect ations and variances connected to such experiments arises. This approa ch seems to throw light upon several controversial questions in the th eory of mixed models. Also, it gives a framework for discussing the ch oice of conditioning in models.