In a fractional-factorial design, effects for which the information obtained are identical.
Note: In a two-level design, the product of the coded levels for the aliased effects are equal.
Example: If there are four factors in a design: \(\rm{A,\ B,\ C,\ D}\) then the main effect of \(\rm{A}\) can be aliased with the three-way effect \(\rm{B} \times \rm{C} \times \rm{D}\). So for the run that has \(\rm{B} = -1\), \(\rm{C} = -1\), \(\rm{D} = +1\), then \(\rm{A}\) must \(= +1\).
Source:
PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 413 (https://doi.org/10.1515/pac-2015-0605)