Split-Plot Designs :: SAS/QC(R) 13.1 User's Guide

Split-Plot Designs

As discussed in the section Structure of General Factorial Designs, for a design with q-level factors in $q^ m$ runs, the FACTEX procedure usually treats the first m factors of the design as the run-indexing factors, and computes the levels of all other factors as linear combinations of these over the Galois field of order q. However, when you restrict the design’s randomization by using the BLOCKS UNITS=() option and UNITEFFECT statements to specify unitfactors and uniteffects, PROC FACTEX instead computes the levels of all factors (including the first m) in terms of underlying plot-indexing pseudo-factors that are distinct from those named in the FACTORS statement. These plot-indexing pseudo-factors are denoted [i], for i=1, …, m, and they are associated with unitfactors as follows: If the BLOCK UNIT=() specification has the form

block units=(Stage1= $n_1$ Stage2= $n_2 \ldots$ );

where $n_1 = q^{k_1}$ , $n_2 = q^{k_2}$ , …, then the first unitfactor, Stage1, is identified with all possible interactions between the first $k_1$ plot-indexing pseudo-factors, the second with the next $k_2$ pseudo-factors, and so on. If you save a split-plot design to a data set by using the OUTPUT statement, then the plot-indexing pseudo-factors are also included in the data set with names _1_, _2_, …, up to the base-q logarithm of the number of runs.

The whole-plot and subplot constraints specified by the UNITEFFECT statement define the relation between the plot-indexing pseudo-factors that correspond to the specified uniteffect and the factor effects specified in the WHOLE=() and SUB=() options. In particular, with a BLOCK UNIT=() specification of the previous form, a UNITEFFECT statement of the form

uniteffect Stage1 / whole=(Stage-1-effects);

means that the Stage-1-effects should be aliased only with interactions between the first $k_1$ plot-indexing pseudo-factors, while

uniteffect Stage1*Stage2 / sub=(Stage-2-effects);

means that the Stage-2-effects should not be aliased with interactions between the first $k_1+k_2$ plot-indexing pseudo-factors.