A 23 full factorial design with 2 replications per cell requires runs.

The correct answer is E. 16. Option E (16) is correct because a 2³ factorial design has 2³ = 8 treatment combinations (cells), and multiplying by 2 replications per cell gives 8 × 2 = 16 total runs. Why the distractors are wrong: A (2) is just the number of levels per factor - it ignores the factors and…

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How the community answered

(32 responses)

A
3% (1)
C
6% (2)
D
3% (1)
E
88% (28)

Explanation

Option E (16) is correct because a 2³ factorial design has 2³ = 8 treatment combinations (cells), and multiplying by 2 replications per cell gives 8 × 2 = 16 total runs.

Why the distractors are wrong:

A (2) is just the number of levels per factor - it ignores the factors and replications entirely.
B (3) is only the number of factors, not the number of runs.
C (4) confuses 2³ with 2² = 4, using the wrong exponent.
D (8) is the number of unique treatment combinations (2³), but forgets to multiply by the 2 replications.

Memory tip: Break it into two steps - first calculate the number of cells using the formula levels^factors (here 2³ = 8), then multiply by replications. Think: "cells first, then scale by reps." Forgetting the replication multiplier is the most common trap, which is why D is the most tempting wrong answer.

Topics

#2^3 factorial#replications#run count#DOE

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