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 Theory of Orthogonal Designs

## Block Factors

If your design involves blocks, additional confounding criteria need to be considered. Blocks are introduced into designs by means of block pseudo-factors. (See "Types of Factors" for details.) A design for q-level factors in qs blocks contains s block pseudo-factors. Denoting the levels of these factors for any given run by B1,B2, ... ,Bs, the index of the block in which the run occurs is given by
B1 + qB2 + q2B3 + ... + qs-1Bs
For each block to occur in the design, every possible combination of block pseudo-factors must occur. This can happen only if all main effects and interactions between the block factors are estimable, which leads to yet another criterion for the confounding rules. Moreover, the effects you want to estimate cannot be confounded with blocks. In general,
• no generalized block pseudo-factors can be confounded with zero
• no generalized interactions between block pseudo-factors and effects you want to estimate can be confounded with zero

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