Two-factor designs unable to examine the interactions (part 1).

Two-factor designs are quite commonly used in scientific research. If the two factors have interactions, research designs like the factorial design and the orthogonal design can be adopted; however, these designs usually require many experiments. If the two factors have no interaction or the interaction is not statistically significant on result in theory and in specialty, and the measuring error of the experimental data under a certain condition (usually it is one of the experimental conditions which is formed by the complete combination of the levels of two factors) is allowed in specialty, researchers can use random block design without repeated experiments, balanced non-complete random block design without repeated experiments, single factor design with a repeatedly measured factor, two-factor design without repeated experiments and two-factor nested design. This article introduced the first three design types with examples.