Discrete variations on two levels

Often the discrete variations are an alternative choice between two varieties, e.g. two different catalysts, two different solvents, two different types of equipment, two different reagents etc. In such cases, the approach is straightforward and it will be possible to establish polynomial response functions to evaluate the effects also of discrete variations. The trick is to use a dummy variable and assign an arbitrary value of +1 or -1 to the alternative choices. It is then possible to fit a polynomial model to the experimental results obtained for different settings of the experimental variables. 

Models which can be used to explore discrete variations are 

A systematic variation of y due to a discrete variation will be picked up as a significant linear coefficient. A significant cross-product coefficient for a discrete variable and a continuous variable will describe how the influence on y of the continuous variable is modified by the discrete change. It is also possible to have interaction effects between discrete variables. For instance, one catalyst may work well in one solvent, but may be totally useless in another. 

It is not possible to use quadratic models which contain square terms of the discrete variables. It is impossible to detect any curvature from only two settings, and quadratic terms would therefore make no sense. 

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