APA Dictionary of Psychology

a research study involving two or more independent variables in which every possible combination of the levels of each variable is represented. For instance, in a study of two drug treatments, one (A) having two dosages and the other (B) having three dosages, a complete factorial design would pair the dosages administered to different individuals or groups of participants as follows: A₁ with B₁, A₁ with B₂, A₁ with B₃, A₂ with B₁, A₂ with B₂, and A₂ with B₃. Compare fractional factorial design.