What are confounding and alias structure?

Aliasing, also known as confounding, occurs in fractional factorial designs because the design does not include all of the combinations of factor levels. For example, if factor A is confounded with the 3-way interaction BCD, then the estimated effect for A is the sum of the effect of A and the effect of BCD. You cannot determine whether a significant effect is because of A, because of BCD, or because of a combination of both. When you analyze the design in Minitab, you can include confounded terms in the model. Minitab removes the terms that are listed later in the terms list. However, certain terms are always fit first. For example, if you include blocks in the model, Minitab retains the block terms and removes any terms that are aliased with blocks.

The alias structure describes the confounding pattern that occurs in a design. Terms that are confounded are also said to be aliased.

The key to the alias structure is the identity statement, for example, I + ABCDE. To determine which effects are confounded, multiply the term of interest by the identity statement and then eliminate the squared terms. For example, to determine the term that BC is confounded with:

(BC)(I + ABCDE) = BC + AB 2C 2DE = BC + ADE

Therefore, BC and ADE are confounded with each other.