# Difference between confounding and aliasing in $2^k$ factorial design

In statistics, particularly in experimental design, what is the difference between confounding and aliasing in $$2^k$$ factorial designs? Also how is a principal block related to the two concepts? I've been looking into the topic recently but there doesn't seem to be a clear difference between them?

• I think that confounding and aliasing are synonyms. If you have some reference saying otherwise, please tell us. Commented Mar 28, 2017 at 15:25

I think Confounded must occur with blocking. The simplest example is $$2^{k}$$ factorial design design with 2 blocks and $$2^{k-1}$$ Experimental Units or runs each block. We will select one effect(usually the highest-order interactions) confounded with the block factor, which means the selected effect cannot be separated from the effect of block factor.

Alias is caused from the defining relation (generator/word) in fractional factorial designs. Take the $$2^{3-1}$$ fractional factorial design for example. If the main effect A is aliased with the 2-factor interaction effect BC, then we actually estimate these two effects together. We can separate these two effects through running the other half of that fractional factorial design. Then after combining these two fractional factorial design, we will have actually a $$2^{3}$$ factorial design with two blocks. However, the 3-order interaction ABC is still confounded here.