ABSTRACT
This chapter develops factor effects notation for factorial models. The cell means model is an example of a statistical model for a factorial design. The cell means model formalizes the assumption that the response for each combination of factor levels is centered about a mean and has some random variation about that mean. The chapter recasts models in terms of factor effects, showing how this can partition mean response among main effects and interactions for multi-factor experiments. Since some experiments are incomplete, by design or by chance, it examines connected cells to show how the pattern of empty cells can limit the range of meaningful comparisons. Sometimes a scientist is interested in comparing group means directly in an experiment involving several factors. The chapter identifies the estimable functions for the one-factor and two-factor effects models while introducing the more general concept of estimability in linear models.
