Compute the average effect of X3:

Question

Options

• A+12
• B-3
• C4
• D+15
• Enone of the above

• A
  7% (2)
• B
  86% (24)
• C
  4% (1)
• E
  4% (1)

Explanation

Option B (-3) is correct because the average effect of X3 is computed by taking the contrast associated with X3 - the difference between the mean responses at X3's high level versus its low level - which yields -3, indicating that increasing X3 decreases the response by 3 units on average.

Option A (+12) is wrong because +12 represents the average effect of a different factor (likely X1 or X2), not X3 - a common mix-up when reading effects from a contrast table. Option C (4) is incorrect because it corresponds to an interaction effect (e.g., X1×X3 or X2×X3), not the main effect of X3 alone. Option D (+15) is also from a different factor's effect or a total sum, making it irrelevant to X3's standalone average effect. Option E is eliminated because B is a valid computed answer.

Memory tip: When computing average effects in factorial designs, track which column or contrast belongs to which factor before dividing - the most common exam mistake is reading the right number from the wrong row or column.

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