|Theory of Orthogonal Designs
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
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,
B1 + qB2 + q2B3 + ... + qs-1Bs
- no generalized block pseudo-factors can be confounded with
- no generalized interactions between block pseudo-factors and
effects you want to estimate can be confounded with zero
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