Factorial Design

Identification

One way to identify factorial designs is by the number of factors involved. Although there is no limit to the number of factors, two-factor and three-factor designs are most common. Occasionally, [Page 475]a researcher will use a four-factor design, but these situations are extremely rare. When a study incorporates a large number of factors, other designs are considered, such as regression.

Another way to identify factorial designs is by the number of levels for each factor. The simplest design is a 2 × 2, which represents two factors, both of them having two levels. A 3 × 4 design also has two factors, but one factor has three levels (e.g., type of reward: none, food, money) and the other factor has 4 levels (e.g., age: 6–8 years, 9–11 years, 12–14 years, 15–16 years). A 2 × 2 × 3 design has three factors; for example, gender (2 levels: male, female), instructional method (2 levels: traditional, computer-based), and ability (3 levels: low, average, high).

In a factorial design, each level of a factor is paired with each level of another factor. As such, the design includes all combinations of the factors’ levels, and a unique subset of participants is in each combination. Using the 3×4 example in the previous paragraph, there are 12 cells or subsets of participants. If a total of 360 participants were included in the study and group sample sizes were equal, then 30 young children (ages 6 to 8) would receive no reward for completing a task, a different set of 30 young children (ages 6 to 8) would receive food for completing a task, and yet a different set of 30 young children (ages 6 to 8) would receive money for completing a task. Similarly, unique sets of 30 children would be found in the 9–11, 12–14, and 15–16 age ranges.

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