# Statistics Dictionary

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### Factorial Experiment

A factorial experiment allows researchers to study the joint effect of two or more factors on a dependent variable.

With a full factorial design, the experiment includes a treatment group for every combination of factor levels. Therefore, the number of treatment groups is the product of factor levels. For example, consider the full factorial design shown below:

A1 A2
B1 B2 B3 B1 B2 B3
C1 Group 1 Group 2 Group 3 Group 4 Group 5 Group 6
C2 Group 7 Group 8 Group 9 Group 10 Group 11 Group 12
C3 Group 13 Group 14 Group 15 Group 16 Group 17 Group 18
C4 Group 19 Group 20 Group 21 Group 22 Group 23 Group 24

Factor A has two levels, factor B has three levels, and factor C has four levels. Therefore, the full factorial design has 2 x 3 x 4 = 24 treatment groups.

Note: Unlike full factorial experiments, fractional factorial experiments include only a subset of possible treatment groups.

 See also: What is a Full Factorial Experiment? | ANOVA With Full Factorial Experiments