In factorial design experiments, fractionating involves using a subset of the full set of experimental runs. A
242^424 full factorial experiment involves 16 runs, and fractionating this to 2412^{4-1}241 results in 8 runs.
* 90% Fraction:
* Incorrect, as this would imply a fractional design close to the full factorial, but it is not standard terminology.
* 75% Fraction:
* The correct answer as 2412^{4-1}241 implies a design that uses 816\frac{8}{16}168 or 50% of the full factorial runs. However, in common terminology, a fractionated design resulting in fewer
* runs (half of the runs) is considered a 50% fraction. Therefore, this fractionation corresponds to a
50% fraction or half fraction.
* Fraction:
* Too vague, as it does not specify the fraction size.
* Fraction:
* Duplicates "fraction."
Therefore, the correct fractional reduction is to a 50% fraction, which is commonly used in design of experiments. The proper fraction designation in this case should be 50%, not 75%.
References: Design of experiments (DOE) principles.