# 2x2x2 (reduced) design to study main effects

I'm at the point of conducting a 2x2x2 factorial design to study corporate adoption decisions. I am only interested in the main effects and run a ANCOVA. This experiment is only one part of a bigger survey. I am really not an expert in statistics and I haven't found a similar simplified study for orientation.

Do I really only need to test three conditions (001, 010, 100) or also include a control setting (000)? Atzmüller, Steiner 2010 proposed a fractional vignette design, such that all levels of each factor are equally often represented and specific two-way interactions.

a0b0c0
a1b1c0
a1b0c1
a0b1c1


When is such a design appropriate?