It reveals interactions of factors. This often proves to be the key to understanding a process. The basic principles of two-level factorial design can be explained in the example of making microwave popcorn. It s nearly impossible to get every kernel of corn to pop. Brand is a categorical factor one type of popcorn or another.
Time is a numerical factor because it can be adjusted to any level.
Power could be set to any percent of the total available, so it s also a numerical factor. If this experiment is attempted, do some range finding on the high level for time. The symbols for categorical factor levels are arbitrary. Taste was determined by a panel of testers who rated the popcorn on a scale of 1, worst, to 10, best. The ratings were averaged and multiplied by 10.