On Analysis of Saturated Unreplicated Factorial Designs

Due to cost and technology, in many industrial applications, unreplicated factorial designs become more and more popular. Frequently, these designs are saturated. The analysis of saturated unreplicated factorial designs can be difficult, while the effects can be usually estimated by contrasts, there are no degrees of freedom left to estimate the error variance, and then the normal ANOVA can be no more used to test significant effects. This paper reviews various methods for analyzing these designs that were developed in the past more than 40 years. Some problems and future research in this field are also discussed.