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How to Develop the Formulas for the Main and the Interaction Effects of the Basic 22 Factorial Design?
How to Develop the Formulas for the Main and the Interaction Effects of the Basic 22 Factorial Design?
The calculation of the effects from a 22 factorial design of experiment is described with examples in Video 2 (both Video 1 and are the same Video 2).
Video 2. Introduction to 2K Factorial Design of Experiments DOE and Formula Equation Explained with Examples.
Method 1. The Basic
Method 1. The Basic
The calculation of the main effect A was described in the Module 5 Factorial Design of Experiments. The main effect of A is calculated by subtracting the average responses at the low-level from the average responses at the high-level.
Therefore, the main effect of the temperature factor can be calculated as in Equation 2.
Equation 2
Using the treatment combination notations, the Equation 2 can be written as in Equation 3, and therefore, the Equation 4.
Equation 3
Equation 4
Similarly, the equations for the main effect of B and the interaction effect of AB can be developed for the 22 design of experiments.
Equation 5
Equation 6
Method 2. The -1/+1 Coding System
Method 2. The -1/+1 Coding System
Using the -1/+1 coding system, the total effect can also be calculated by simply multiplying the factor A column with the treatment combination column (Table 1), which results in the Equation 7. Total effect of
Equation 7
As there are two replications for A, the average effect is calculated as in Equation 8.
Equation 8
Similarly, the equations for the main effect of B and the interaction effect of AB can be developed as in Equation 5 and Equation 6.
Method 3. The Commonsense System
Method 3. The Commonsense System
Another way of developing the equation for the main effect of factor A is subtracting all treatment combinations without “a” in them from all the treatment combinations that contain “a” in them. Think about all the experimental units that received a fertilizer as compared to those did not receive the fertilizer. Therefore, the main effect of
Similarly, the equations for the main effect of B and the interaction effect of AB can be developed as in Equation 5 and Equation 6.
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