Full Factorial vs. Classical Experiments

In planning experiments and analyzing the results, the experimenter is confronted with a series of decisions (see Table 3.1). 

As little as three factors can confront the investigator with an intractable situation if he chooses to proceed classically. One way out is to use the factorial approach, which can just be visualized for three factors. An example from process optimization work will illustrate the concept. Assume that temperature, the excess concentration of a reagent, and the pH have been iden- 

A problem with the simplex-guided experiment (right panel) is that it does not take advantage of the natural factor levels, e.g., molar ratios of 1 0.5, 1 1, 1 2, but would prescribe seemingly arbitrary factor combinations, even such ones that would chemically make no sense, but the optimum is rapidly approached. If the system can be modeled, simulation might help. The dashed lines indicate ridges on the complex response surface. The two figures are schematic. 

Program FACTORS in Section 5.2.3 lists the exact procedure, which is only. sketched here. Table 3.2, for each factor and interaction, lists the observed effect, and the specific effect, the latter being a slope or slopes that make(s) the connection between any factor(s) and the corresponding effect. A r-test is conducted on the specific effects, i.e., t = Ej/(Ax se), where Ej is the observed effect y, - yi, se its (estimated) standard deviation, and Ax the change in the factor(s) that produced the effect. If t is larger than the 

Because the preceding factor experiment suggests a, b, c, and abc as independent variables, cf. bottom row in Table 3.2, the data table would take on the form  

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