| Theory of Orthogonal Designs |
General Criteria
The criteria for an orthogonally confounded qk design reduce to requiring
that no generalized interactions in a certain set
M can be confounded with zero.
(See "Structure of General Factorial Designs"
for a definition of generalized interaction.)
This section presents the
general definition of M. First, define three sets, as follows:
- E
- the set of effects that you want to estimate
- N
- the set of effects you do not want to estimate
but that have unknown nonzero magnitudes
(referred to as nonnegligible effects)
- B
- the set of all generalized interactions
between block pseudo-factors
Furthermore, for any two sets of effects A and B, denote by
A×B the set of all generalized interactions
between the effects in A and the effects in B.
Then the general rules for creating the set of effects M that are
not to be confounded with zero are as follows:
- Put E in M. This ensures that all
effects in E are estimable.
- Put E×E in M. This ensures
that all pairs of effects in E are unconfounded with
each other.
- Put E×N in M. This ensures
that effects in E are unconfounded with effects in
N.
- Put B in M. This ensures that all
qs blocks occur in the design.
- Put E×B in M. This ensures
that effects in E are unconfounded with blocks.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
