Explain the purpose of a 2k full factorial design. Answer: The purpose of a 2k full factorial design is to understand the relationships between a set of Xs each with only two levels, and the…

Question

Options

• Amain factor effects
• Btwo way interactions
• Cthree way interaction
• Dall of the above

• A
  6% (3)
• B
  2% (1)
• C
  4% (2)
• D
  88% (44)

Explanation

Option D is correct because a 2k full factorial design is explicitly designed to estimate all effects simultaneously - main effects, two-way interactions, and higher-order interactions (including three-way). Options A, B, and C are not "wrong" in isolation - they are each real outputs of the design - but none alone captures the full purpose, making them incomplete answers rather than incorrect ones. The power of a full factorial over a fractional factorial is precisely that nothing is aliased or sacrificed: every factor combination is tested, so interactions of any order can be independently estimated. A helpful memory tip: think of "full" as meaning full coverage - if it's full factorial, you get the full picture across all main effects and all interaction levels, which is why D ("all of the above") is always the right framing for its purpose.

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