Multifactor designs able to examine the interactions.

Multifactor designs that are able to examine the interactions include factorial design, factorial design with a block factor, repeated measurement design; orthogonal design, split-block design, etc. Among all the above design types that are able to examine the interactions, the factorial design is the most commonly used. It is also called the full-factor experimental design, which means that the levels of all the experimental factors involved in the research are completely combined, and k independent repeated experiments are conducted under each experimental condition. The factorial design with a block factor can also examine the influence of a block factor formed by one or more important non experimental factors based on the factorial design. This article introduces the factorial design and the factorial design with a block factor by examples.