A great tasting Lemonade is a result of an experimentation.
2 level factorial designs are the first resort for anybody making their first attempt at Design of Experiments (DoE). Basically, these designs consist of all combinations of each factor at its high and low levels (Full factorial). However, these designs do not work out for some industries in which the product under investigation is made up of several components or ingredients e.g. Chemicals, Foods, Pharmaceuticals, etc. In these cases, the response depends on proportions of different ingredients in the mixture. The quantities of components, measured in weights, volumes, or some other units, add up to a common total. In contrast, in a factorial design, the amount of each factor is varied, and the sum of the amounts for each run need not be constant.
Let us understand this with a simple example of making Lemonade.
Lemonade components and their ranges:
The response is the taste rating scaled from 1 to 10, 1 being worst to 10 being the best.
Let us first try to do a Factorial experiment. The design layout along with the results of the taste ratings are given in the table below.
Design Layout: Factorial design
Have a look atthe experiments numbered 1 and 4. Do you think Experiment 1 and 4 are the same? Well, they only differ in the volume of the lemonade as a result of mixing the two ingredients. The proportions remain the same. Obviously, they will taste the same as well. Thus, it makes more sense to look at taste as a function of the proportion of lemonade concentrate to water, not the amount.