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Unformatted text preview: Math 208  3 Way ANOVA and more 1 MultiFactor Designs The extension of the ANOVA model from a twofactor ANOVA to a kfactor ANOVA is fairly straight forward. We look at a 3factor ANOVA as our start ing point, and see that, as expected, things get slightly more messy, though in foreseeable ways. 1.1 Our Model Y ijkl = μ + α i + β j + γ k + ( αβ ) ij + ( αγ ) ik + ( βγ ) jk + ( αβγ ) ijk + ² ijkl where we have 3 main effects, 3 twoway interactions, and now a threeway interaction as well. In a balanced design of n observations, we have n T = nabc total observations. The main effects are defined in exactly the same way as before, for instance: α i = μ i ·· μ ··· As we would expect, the main effects for factor C are γ k = μ ·· k μ ··· The twofactor interactions describe how the means deviate from the additive model if we average over one of the factors. It is perhaps useful to think of the data being entered in a 3dimensional table, resembling a cube, with each cell being a smaller cube (in the same way a 2 dimensional table is a square with the cells being smaller squares). If we were to average over a particular variable, we now have a 2dimensional table, a situation we are used to. If the main effects do not describe the cell means, then there are twoway interactions present. We define these terms as:there are twoway interactions present....
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This note was uploaded on 01/30/2011 for the course MAT 219 taught by Professor Ab during the Spring '10 term at Conn College.
 Spring '10
 AB
 Math

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