Split-Plot Designs

As discussed in the section Structure of General Factorial Designs, for a design with -level factors in runs, the FACTEX procedure usually treats the first 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 . 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 ) 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= Stage2=);

where , , ..., then the first unitfactor Stage1 is identified with all possible interactions between the first plot-indexing pseudo-factors, the second with the next 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- logarithm of the number of runs.

The wholeplot and subplot constraints specified by the UNITEFFECT statement define the relation between the plot-indexing pseudo-factors corresponding 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 only be aliased with interactions between the first 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 plot-indexing pseudo-factors.