FAQ/HierarchicalDesigns - CBU statistics Wiki
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# Sums of Squares for Hierarchical Designs

We will explore the Expected Mean Squares for a standard Split Plot Design.

Suppose $$G$$ levels of a factor $$A$$ with $$K$$ families $${\F_text{gk},\text{k}=1\ldots K\}$$ nested within each group $$\{A_text{g},text{g}=1\ldots G\}$$, and within that family there are $$\mbox{n}_text{jk}$$ individuals on whom measurements are made.

Then pooling the K variances we have

$$\mbox{Pooled Variance V = } \frac{\sum_text{k}text{K} (n_text{k}-1) \mbox{V}_text{k}}{\sum_text{k}text{K} (n_text{k} -1)}$$

and we can use this pooled variance to obtain the standard error of the mean since

$$\mbox{Pooled Mean Standard Error = } \sqrt{ \frac{\mbox{V}}{\sum_text{k}^text{K} n_text{k}} }$$

None: FAQ/HierarchicalDesigns (last edited 2013-03-08 10:17:58 by localhost)