Factorial experiment

In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called the response variable. Each factor is tested at distinct values, or levels, and the experiment includes every possible combination of these levels across all factors. This comprehensive approach lets researchers see not only how each factor individually affects the response, but also how the factors interact and influence each other.

Often, factorial experiments simplify things by using just two levels for each factor. A 2x2 factorial design, for instance, has two factors, each with two levels, leading to four unique combinations to test. The interaction between these factors is often the most crucial finding, even when the individual factors also have an effect.

If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional factorial design. This method strategically omits some combinations (usually at least half) to make the experiment more manageable.

These combinations of factor levels are sometimes called runs (of an experiment), points (viewing the combinations as vertices of a graph), and cells (arising as intersections of rows and columns).