Explain how the coefficient pattern for a 23 full factorial design is used to estimate the effects of one interaction factor (XiXj) on the CTQ. Answer: Multiply the signs of Xi and Xj to create a…

Question

Options

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

• A
  10% (3)
• B
  6% (2)
• C
  26% (8)
• D
  58% (18)

Explanation

Option D is correct because the coefficient pattern method described - multiply factor signs to generate a contrast column, sum the CTQ values at each sign level, then divide the difference by the number of plus signs - is identical for all effect types in a 2³ design: main effects (single-factor columns already have + / − signs), two-way interactions (multiply two columns), and the three-way interaction (multiply all three columns). Options A, B, and C are each only partially correct; they describe subsets of where the method applies, making them incomplete answers rather than wrong facts - the method doesn't change based on the order of the interaction, only the column you construct changes.

Memory tip: Think of the coefficient pattern as a universal formula - "same recipe, different ingredients." Whether you're estimating X₁ alone (main effect), X₁X₂ (two-way), or X₁X₂X₃ (three-way), you follow the exact same steps; only the number of factor columns you multiply together differs. If a method works for interactions, it works for all interactions.

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