Statistical design of experiments the factorial method

Experimental design in statistics

This article is about factorial design. For factor loadings, see Factor analysis. For factorial numbers (n!), see Factorial.

In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.

A full factorial design may also be called a fully crossed design.

Factorial experiment - Wikipedia

Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.

For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2×2 factorial design.

In such a design, the interaction bet