A 23 full factorial design can be physically represented by which shape?

Question

Options

• Asquare
• Bcube
• Crectangle
• Dcircle
• Enone of the above

• A
  5% (1)
• B
  89% (17)
• E
  5% (1)

Explanation

A 2³ full factorial design involves 3 factors, each tested at 2 levels (low and high), producing 2³ = 8 experimental runs. Each factor maps to one axis in 3D space, and the 8 runs correspond exactly to the 8 corners of a cube - making B correct.

Why the distractors are wrong:

• A (square): A square has only 4 corners, representing a 2² design (2 factors, not 3).
• C (rectangle): Also 2D with 4 corners; rectangles represent 2-factor designs with unequal spacing, not a standard 2³.
• D (circle): A circle has no discrete corner points and doesn't map to any standard factorial design geometry.
• E (none of the above): Incorrect because the cube is a well-established geometric representation.

Memory tip: Match the exponent to the number of dimensions - 2¹ = line (2 points), 2² = square (4 corners), 2³ = cube (8 corners). The superscript tells you the shape's dimension.

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