Drawbacks of using sign tables

The calculations involved in the evaluation of factorial designs by using sign tables rely on an unrealistic assumption, viz. that each experiments was conducted exactly as was specified by the design. For instance, that the temperature was adjusted exactly to its high and low levels. In practice, this is never obtained in synthetic chemistry. The variables can be adjusted fairly close to the specified levels, but over the series of experiments, there will always be small differences between the runs. It is therefore better, and more honest, to use the settings actually used in the evaluation of the experiments. For this, the appropriate tool is multiple linear regression which is used to fit response surface models to the experimental data. This technique is described in the next section. 

A method often used for hand-calculation of effects from factorial designs is the Yates algorithm.[2] As this algorithm also assumes that the levels of the variables are exactly as specified by the design. It is therefore suggested that it should not be used to the evaluation of synthesis experiments. 

Least squares fit of response surface models to experunents in factorial designs 

A factorial design can be used to fit a response surface model to the experimental results. In this case, the effects will be the corresponding model parameters. To achieve this, the factors are scaled through a linear transformation to design variables, x, as was described in section 3.4.2, see also Fig. 5.2. 

The experimental design will be described by a design matrix. As an example a 2 design is shown in Table 5.4. 

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