Designs which permits two or more questions to be addressed in the investigation.
The easiest factorial design is one in which each of the two treatments or interventions are present or absent, so that subjects are splitted into four groups; those receiving neither of the treatment, those having the first treatment only, those having the second treatment only and those receiving both the treatments. Such designs enable possible interactions between the factors to be investigated. A very significant special case of the factorial design is that where each of k factors of interest contains only two levels; these are generally known as 2k factorial designs. Particularly significant in industrial applications of the response surface methodology. A single replicate of the 2k design is sometimes called as an unreplicated factorial.