e-Statistics

Additive Model on Two-Way Layout

An experiment involving one-way layout with blocks is called bf randomized block design for which agricultural experiments provide a classic example. To compare the effects of $ k$ different fertilizers (``treatments,'' or ``factor levels''), $ b$ plots of land (or ``blocks'') are selected, and each of them is divided into $ k$ plots; this is viewed as a multi-sample generalization of paired experiment. Within each block, the assignment of fertilizers to plots is made at random, which helps to ensure against unintentional bias. Then data of size $ n$ are obtained for each combination of treatment and block, and summarized in the following table.

Treatment Block-1 . . . . . . . Block-b Sample size
1 $ X_{11 \cdot}$ . . . . . . . $ X_{1b \cdot}$ $ b$
$ \vdots$ $ \vdots$ . . . . . . . $ \vdots$ $ \vdots$
k $ X_{k1 \cdot}$ . . . . . . . $ X_{kb \cdot}$ $ b$

Each $ X_{ij \cdot}$ consists of $ n$ measurements $ X_{ijl}$, $ l=1,\ldots,n$.


© TTU Mathematics