Explain how the standard order matrix for a 23 full factorial design is used to estimate the effects of one main factor on the CTQ. Answer: Add up the values of the CTQ for which the X is +, then add

Question

Options

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

• A
  6% (1)
• B
  6% (1)
• C
  12% (2)
• D
  76% (13)

Explanation

Option D is correct because in a 2³ full factorial design, the same contrast procedure - summing CTQ values at "+" levels, subtracting the sum at "−" levels, and dividing by the number of plus signs - is used identically to estimate all effects: main effects, two-way interactions, and the three-way interaction. The interaction columns are simply derived by multiplying the signs of their constituent factor columns row-by-row (e.g., the X1×X2 column = X1 signs × X2 signs), then the same arithmetic applies. Options A, B, and C are each individually true but incomplete - choosing any one of them alone ignores that the same formula generalizes to every column in the design matrix. Remember this with the phrase "same math, different columns": whether the column belongs to a main effect or an interaction, you always sum the pluses, subtract the minuses, and divide by n/2.

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