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The 2K 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 2K design of experiments. More specifically, this experiment should be named as the completely randomized 2K factorial design of experiments. Recent popular textbooks on the design of experiment refer this design as the 2K design (Box et al., 2005; Montgomery, 2019) , while the earlier texts refer the design as 2n design (Hinkelmann & Kempthorne, 2008; Kempthorne, 1952; Yates, 1978), 2f (Hicks, 1964), 2p, and so on. However, recently, 2K 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 22 design, which is the basic to all 2K factorial design of experiments. The formulas or equations for the 22 will be shown first and then it will be generalized for the 2K factorial design of experiments. The process of formula development will provide us with a behind the scene picture of a 2K design. Understanding this step will significantly impact learning the 2K 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 2K factorial design of experiments. Moreover, for a detail understanding of the concepts of the 2K 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.
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