Factorial Experiment

Abstract

Basic experimental designs what we have discussed in the previous chapter take care of one type/group of treatments at a time. If an experimenter wants to test more than one type/group of treatments, then more than one set of experiments are required to be set, thereby requiring a huge amount of resources (land, money, other inputs) and time. Even with ample resources and time, desirable information may not be obtained from simple experiments. Suppose an experimenter wants to know not only the best treatment from each of the two sets of treatments but also wants to know the interaction effects of the two sets of treatments. This information cannot be obtained by conducting two separate sets of simple experiments with two groups/types of treatments. Let us suppose an experimenter wants to know (i) the best varieties among five newly developed varieties of a crop (ii) the best dose of nitrogenous fertilizer for the best yield of the same crop and (iii) also wants to know which variety among the five varieties under which dose of nitrogen provides the best yield (i.e., variety and dose interaction effect). The first two objectives (i.e., the best variety and best dose of nitrogen) can be accomplished by framing two separate simple experiments (one with five varieties and the other one with different doses of nitrogen with a single variety), but the third objective, i.e., interaction of varieties with different doses of nitrogen, cannot be obtained from these two experiments. For this purpose we are to think for an experiment which can accommodate both the groups of treatments together. Thus, in agriculture and other experiments, the response of different doses/levels of one group of treatments (factor) is supposed to vary over the different doses or levels of other set(s) of treatments (factor(s)). Factorial experiments are such a mechanism in which more than one group (factor) of treatments can be accommodated in one experiment, and from the experiment, not only the best treatment in each group of treatments could be identified but also the interaction effects among the treatments in different groups could also be estimated.