Factorial experiment

A factorial experiment tests every combination of selected levels of two or more factors. It estimates each factor’s effects and whether their effects depend on one another.

Factor: An independent variable whose levels define experimental conditions. Factors are the variables whose levels are systematically combined.
Randomization: The assignment of experimental units to conditions by chance. Random assignment helps separate treatment effects from systematic confounding.
Full factorial design: A design that includes every combination of the specified factor levels. This is the complete form of the factorial experiment defined here.
Design of experiments: The planning of controlled studies to learn how inputs affect measured outcomes. Factorial experiments are a major family within experimental design.
Factor level: A value or category assigned to an experimental factor. Each factor level contributes to the combinations tested.
Replication: The application of the same experimental condition to multiple independent units. Replication provides information about variability within treatment combinations.
Fractional factorial design: A design that tests a selected fraction of all possible factor-level combinations. It reduces experimental runs but can alias effects.
Clinical trial: A study in human participants that evaluates health-related interventions or outcomes. Factorial trials can test combinations of interventions within one study.
Treatment combination: A specific combination of factor levels assigned in an experiment. Each treatment combination is one condition in the factorial design.
Experimental unit: The smallest unit independently assigned to an experimental condition. The unit of assignment determines what counts as an independent replicate.

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