Abstract
Ever since the founding work by Finney (1945), it has been widely known and accepted that aliased effects in two-level regular designs cannot be “de-aliased” without adding more runs. A result by Wu in his 2011 Fisher Lecture showed that aliased effects can sometimes be “de-aliased” using a new framework based on the concept of conditional main effects (CMEs). This idea is further developed in this paper into a methodology that can be readily used. Some key properties are derived that govern the relationships among CMEs or between them and related effects. As a consequence, some rules for data analysis are developed. Based on these rules, a new CME-based methodology is proposed. Three real examples are used to illustrate the methodology. The CME analysis can often lead to models with fewer effect terms and smaller p values for the selected effects. Moreover, the selected CME effects are often more interpretable.
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