$2^{5-2}$ Design : Alias Structure

Question

$2^{5-2}$ Design

Design Generators: $D=AB\quad E=AC$

Defining Relation: $I=ABD=ACE=BCDE$

$$\text{Aliases}$$ $$A=BD=CE=ABDE$$ $$B=AD=ABCE=CDE$$ $$C=ABCD=AE=BDE$$ $$D=AB=ACDE=BCE$$ $$E=ABDE=AC=BCD$$ $$BC=ACD=ABE=DE$$ $$CD=ABC=ADE=BE$$ But the alias structure in the book Design and Analysis of Experiments by Douglas C. Montgomery [Appendix XII (c)] is as following:

$$\text{Aliases}$$ $$A=BD=CE$$ $$B=AD=CDE$$ $$C=AE=BDE$$ $$D=AB=BCE$$ $$E=AC=BCD$$ $$BC=DE=ACD=ABE$$ $$CD=BE=ABC=ADE$$

Instead of $A+BD+CE+ABDE$, this is $A+BD+CE$ in the book and so on.

• Why ?

Answer 1

I think he's just not showing the 4- and 5-way interactions, for brevity and assuming people won't be too concerned about them

Answer 2

Interaction of order IV or higher are not written because they are usually not significant. This principle is called "sparsity-of-effects principle" and it is explained in Design and Analysis of Experiments by Douglas C. Montgomery.