# What is a 2K Factorial Design of Experiment?

The 2^{K} factorial design of experiment is described with examples in Video 1.

Video 1. Introduction to 2K Factorial Design of Experiments DOE Formula Equation Explained with Examples.

As the *factorial design of experiments* is primarily used for screening variables, using only two levels are enough to determine whether a variable is significant to affect a process or not. If k number of variables/factors are studied to determine/screen the important ones, the total number of treatment combinations for a k number of factors can be calculated as in Equation 1. Therefore, this screening technique is known as the *2 ^{K} design of experiments*. More specifically, this experiment should be named as the

*completely randomized 2*. Recent popular textbooks on the design of experiment refer this design as the

^{K}factorial design of experiments*2*(Box et al., 2005; Montgomery, 2019)

^{K}design*, while the earlier texts refer the design as 2*

^{n}design (Hinkelmann & Kempthorne, 2008; Kempthorne, 1952; Yates, 1978), 2

^{f }(Hicks, 1964), 2

^{p}, and so on. However, recently, 2

^{K}name has been popular for the

*factorial design of experiments*with multiple factors with two levels for each factor.

Equation 1

The design is conducted very systematically and will be explained here, so that no data is wasted even if the insignificant variables are deleted from the study. Table 1 shows the layout, data structure and the coding systems for the levels of the factors of a 2^{2} design, which is the basic to all 2^{K} factorial design of experiments. The formulas or equations for the 2^{2} will be shown first and then it will be generalized for the 2^{K} factorial design of experiments. The process of formula development will provide us with a behind the scene picture of a 2^{K} design. Understanding this step will significantly impact learning the 2^{K} design and analysis of an experiment and interpreting the results in the context of the problems. Moreover, the formula development process will be extremely useful in understanding the *Module 7 fractional factorial design,* which is the ultimate goal of learning the *factorial design of experiments. *

Statistical software such as MS Excel, Minitab, SAS, and SPSS will be demonstrated for both design and analysis of the 2^{K} factorial design of experiments. Moreover, for a detail understanding of the concepts of the *2 ^{K} factorial design of experiments, *the manual calculations will be shown using MS Excel without requiring plugging the numbers in the formula. Rather than plugging the numbers (or responses) in the formulas, a method in MS Excel is shown in section 2.4 to produce all necessary results.