Question

Factorial experiments are:

• A. Symmetric experimental designs
• B. Orthogonal experimental designs
• C. Complete experimental designs
• D. Not experimental designs

Hint:

Compare a full factorial layout with a fractional factorial design: one tests every possible treatment combination, the other tests only part of them.

Answer 1

The Correct Option is C

Step 1: Recall what a factorial experiment involves. In a factorial experiment, more than one factor is studied at the same time, and every level of one factor is combined with every level of the other factor(s).

Step 2: If there are factors with \(p, q, r, \ldots\) levels respectively, a factorial experiment lays out all \(p \times q \times r \times \ldots\) possible treatment combinations, not just a subset of them.

Step 3: Because every single combination of levels across all factors is actually tried out (nothing is left out or fractioned), such an experiment is termed a complete experimental design. This is exactly the distinction drawn against a fractional factorial design, where only a chosen fraction of the total combinations is tested.

Step 4: The term "symmetric" factorial experiment refers separately to the case where every factor has the same number of levels (e.g. all factors at 2 levels, a \(2^n\) design), and "asymmetric" is used when the factors have different numbers of levels. Orthogonality is a property of certain designs used for estimation efficiency, not a defining feature of factorial experiments themselves. So neither option 1 nor option 2 describes what a factorial experiment fundamentally is.

Step 5: Hence the correct description of factorial experiments, as a class, is that they are complete experimental designs.

\[\boxed{\text{Complete experimental designs}}\]