3wayANOVA - Math 208 - 3 Way ANOVA and more 1 Multi-Factor...

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Unformatted text preview: Math 208 - 3 Way ANOVA and more 1 Multi-Factor Designs The extension of the ANOVA model from a two-factor ANOVA to a k-factor ANOVA is fairly straight forward. We look at a 3-factor 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 two-way interactions, and now a three-way 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 two-factor 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 3-dimensional 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 2-dimensional table, a situation we are used to. If the main effects do not describe the cell means, then there are two-way interactions present. We define these terms as:there are two-way 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.

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3wayANOVA - Math 208 - 3 Way ANOVA and more 1 Multi-Factor...

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