5.3. Choosing an experimental design
5.3.3. How do you select an experimental design?
188.8.131.52. Randomized block designs
|These designs handle 4 nuisance factors||Hyper-Graeco-Latin squares, as described earlier, are efficient designs to study the effect of one treatment factor in the presence of 4 nuisance factors. They are restricted, however, to the case in which all the factors have the same number of levels.|
|Randomize as much as design allows||
Designs for 4- and 5-level factors are given on this page. These
designs show what the treatment combinations should be for each run.
When using any of these designs, be sure to randomize the
treatment units and trial order, as much as the design allows.
For example, one recommendation is that a hyper-Graeco-Latin square design be randomly selected from those available, then randomize the run order.
|Hyper-Graeco-Latin Square Designs for 4- and 5-Level Factors|
|Designs for 4-level factors (there are no 3-level factor Hyper-Graeco Latin square designs)||
L1 = 4 levels of factor X1 (block)
L2 = 4 levels of factor X2 (block)
L3 = 4 levels of factor X3 (primary)
L4 = 4 levels of factor X4 (primary)
L5 = 4 levels of factor X5 (primary)
N = L1 * L2 = 16 runs
|Designs for 5-level factors||
L1 = 5 levels of factor X1 (block)
L2 = 5 levels of factor X2 (block)
L3 = 5 levels of factor X3 (primary)
L4 = 5 levels of factor X4 (primary)
L5 = 5 levels of factor X5 (primary)
N = L1 * L2 = 25 runs
|Further information||More designs are given in Box, Hunter, and Hunter (1978).|