A 23 full factorial design with 2 replications provides information about:

The correct answer is D. all of the above. Option D is correct because a 2³ full factorial design - with 3 factors each at 2 levels - tests all 2³ = 8 treatment combinations, which provides estimates of every main effect (A, B, C), every two-way interaction (AB, AC, BC), and the three-way interaction (ABC). Options A, B,

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Options

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

How the community answered

(37 responses)

B
3% (1)
C
3% (1)
D
95% (35)

Explanation

Option D is correct because a 2³ full factorial design - with 3 factors each at 2 levels - tests all 2³ = 8 treatment combinations, which provides estimates of every main effect (A, B, C), every two-way interaction (AB, AC, BC), and the three-way interaction (ABC). Options A, B, and C are each partially true but incomplete: they describe only one category of effects the design estimates, making them insufficient answers on their own. The 2 replications add no new factor structure - they simply provide degrees of freedom for estimating pure experimental error, enabling significance tests for all those effects. A good memory tip: "Full factorial = full information." In a full factorial design, no combinations are omitted, so no effects are confounded or hidden - you always get the complete picture, which is exactly what "all of the above" captures.

Topics

#full factorial design#main effects#interactions#2^3 DOE

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