ABSTRACT
In our studies of different experimental layouts, RCBDs the Latin squares, and the Graeco-Latin square designs, we have already learned that experiments are performed to investigate the effects of a factor (an explanatory variable) or a combination of factors on one or more outcome or response variables. However, the experiments did not investigate the effects of all possible combinations of the studied factors on the responses. For instance, we could only use the Graeco-Latin and the Latin square designs to study the effects of factors on responses if we were certain that there were no interactions between the factors in the design. If each of the factors that is investigated in a given design is set at a number of levels, we may wish to study almost every combination of the levels of the factors. A study that aims to investigate the effects of all possible combinations of the levels of the factors in a full design is called a factorial experiment. Of all possible design configurations that could be devised for such a study, a full factorial experiment provides the most efficient way for carrying out such a study. Other ways of carrying out the same investigation may be time-consuming and expensive. They may also require more units to arrive at the same precision as the typical factorial experiment.
