Alias Structure

The alias structure of a design identifies which effects are confounded (or aliased) with each other in the design. Note the difference between alias structure and confounding rules: the confounding rules are used to construct the design, and the alias structure is a result of using a given set of confounding rules. To display the alias structure for a design, use the ALIAS option in the EXAMINE statement.

Examining the alias structure is important because aliased effects cannot be estimated separately from one another. When several effects are listed as equal, the effects are all jointly aliased with one another and form an alias chain or alias string. For example,

Temperature*Moisture=HoldPress*Gage=Thickness*Screw=BoostPress*Time  

is an alias chain that shows the relationship between four 2-factor interactions. If you want separate estimates of Temperature*Moisture and Thickness*Screw, for example, a design with this alias chain would not be acceptable. Designs of even resolution contain one or more such chains of confounded -factor interactions.

By default, the FACTEX procedure displays alias chains with effects up to a certain order , where main effects are order 1, two-factor interactions are order 2, and so on. The value of can be specified in the ALIASING option, or you can use the default calculated by the procedure. Alias chains that are confounded with blocks are displayed with [B] on the left-hand side.