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2.1. exampleswe start with three examples to illustrate the diversity of situations we want to consider, all based on real applicationsfrom our consulting experience.we follow standard practice in using the same notation a for a factor and its main effect, and the notation a, b for theinteraction between factors a and b. hierarchy relationships are denoted as in bailey (2008, chapter 10). in particular:- b 4, a means that factor b is or must be nested in factor a, in other words b must be finer than or equivalent to a andreciprocally, a must be coarser than or equivalent to b, so that each level of b occurs with a single level of a;- a ∧ c denotes the product or infimum of a and c, which is the factor whose levels are the combinations of levels of a andc.note the following two properties:- a ∧ c 4 a and a ∧ c 4, c;- if a 4 b and a 4 c, then a 4 b ∧ c
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