high

Monday, May 21, 2007

 

Nested Design -- unavoidable?

Nested Design

Example : http://www.engr.mun.ca/~llye/PP11%20Nested.ppt#256,1,Nested
also see Nested ANOVA http://udel.edu/~mcdonald/statnested.html

In a nested design, the model spells out as:






Model can be represented in another way:








I think the most significant bit is the df : M.m.n -1 = (M-1) + M(m-1) + Mm(n-1)


The ANOVA table :



My design is not a pure nested design, but a partial nested one. Refer to Analysis of Variance http://www.statgraphics.com/analysis_of_variance.htm

" The General Linear Models procedure is used whenever the above procedures are not appropriate. It can be used for models with both crossed and nested factors, models in which one or more of the variables is random rather than fixed, and when quantitative factors are to be combined with categorical ones. Designs that can be analyzed with the GLM procedure include partially nested designs, repeated measures experiments, split plots, and many others. For example, pages 536-540 of the book Design and Analysis of Experiments (sixth edition) by Douglas Montgomery (Wiley, 2005) contains an example of an experimental design with both crossed and nested factors. For that data, the GLM procedure produces several important tables, including estimates of the variance components for the random factors.


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