Question: Suppose that in a 2^4-1 fractional factorial study with D↔ABC, data analysis leads to the conclusion that the detectable sums of effects are "grand mean plus alias," "A main effect plus alias," "B main effect plus alias," "C main effect plus alias," and "ABC 3-factor interaction plus alias." One plausible interpretation of this is that all of A, B, C, and D have detectable main effects. Further, suppose that α2, β2, and γ2 appear to be positive, while δ2 appears to be negative. What combination of levels of factors A, B, C, and D then has the largest fitted mean? Is this combination represented in the original data set?