THE FACTORIAL PRINCIPLE

In the experimental lay-outs, such as the completely randomised and randomised block designs of Chapter 11, the main object is to compare and estimate the effect of a single set of ‘treatments’ such as different varieties of wheat. The chief purpose of introducing blocks is to make allowance for unwanted but unavoidable heterogeneity. However, as pointed out in section 11.5, we can in some cases use a randomised-block type of analysis for an experiment in which the blocks merely represent the levels of a second factor, such as different types of fertiliser. This raises the whole question of how many factors can be incorporated in a single experimental design, and whether this is or is not a desirable practice.

It is customary in the classical type of scientific experimentation to advocate the investigation of any problem by holding most of the variable factors constant and allowing only one or two to vary in each experiment. If one is largely occupied with fundamental research, where the point is to formulate general laws and test crucial predictions, this procedure of isolating one or two factors at a time has much to recommend it.

If, on the other hand, one is dealing with work that is of a more general nature, such as the prosecution of a plant-breeding programme, then one is essentially concerned to know what happens with a range of combinations of factors.