A multivariate design is necessary

The most common approach to the study of discrete variations in the reaction space is to consider one type of variation at a time. For example The scope of a reaction with regard to substrate variation is often studied by means of a series of test substrates while maintaining the reagent(s) and solvent fixed the influence of solvent variation is studied with one test substrate and with a given reagent, etc. 

Such a study will, however, describe one-dimensional excursions through the reaction space and like any other one-variable-at-a-time study it cannot provide atty information whatsoever on possible interaction effects. 

A moment of reflection reveals that such interactions are not only possible, but are likely to be present in any variation of the reaction systems. Such interactions can give rise both to compensating and to amplifying effects  

The ability to recognize such interaction effects is therefore very important when a new reaction is elaborated, otherwise the potential of the reaction for preparative use may be overlooked. It is therefore necessary to use multivariate strategies to explore the reaction space so that the joint influence of varying the substrate, the reagent(s), and the solvent can be evaluated. This can be accomplished by multivariate designs in the principal properties. These designs will define sub-sets of test systems which can furnish the desired information. The principles are discussed in Chapter 16. 

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