What is a factorial design?

• A. A factorial design studies two or more independent variables simultaneously, examining main effects and interactions.
• B. A factorial design uses a single variable with multiple levels exclusively.
• C. A factorial design randomly assigns participants to all possible combinations but measures only one outcome.
• D. A factorial design ignores interactions and focuses on a single main effect.

Answer: (A)

The main idea being tested is that factorial designs study two or more independent variables at once, allowing us to see both their separate effects and how they interact. By manipulating each factor across its levels and crossing them, you can observe the effect of each variable on the outcome (main effects) and whether the effect of one variable changes depending on the level of another variable (an interaction).

For example, imagine studying how study method (traditional vs spaced) and test difficulty (easy vs hard) influence exam scores. This creates four groups corresponding to every combination. You can tell whether spaced study helps scores overall (a main effect of study method), whether harder tests generally lower scores (a main effect of difficulty), and whether the benefit of spaced study is larger on hard tests (an interaction). Factorial designs are efficient because you gather information about multiple factors and their interplay within a single experiment rather than running separate experiments for each factor.

If a design focuses on just one variable with multiple levels, that isn’t a factorial design. If it’s described as measuring only one outcome or as ignoring interactions, that misses the essence of factorial experimentation, which is precisely about detecting how factors work together.