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Some experiments involve the study of the effects of multiple factors. For such studies, the factorial experimental design is very useful. A full factorial design, also known as fully crossed design, refers to an experimental design that consists of two or more factors, with each factor having multiple discrete possible values or “levels”.
Using this design, all the possible combinations of factor levels can be investigated in each replication. Although several factors can affect the variable being studied in factorial experiments, this design specifically aims to identify the main effects and the interaction effects among the different factors.
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To understand the factorial experimental design, you must be well-acquainted with the following terms:
Factors: This is a broad term used to describe the independent variable that is manipulated in the experiment by the researcher or through selection.
Main Effects: The main effect of a factor refers to the change produced in response to a change in the level of the factor. Therefore the effect of factor A is the difference between the average response at A1 and A2.
Interaction: An Interaction between factors occurs when the difference in response between the levels of one factor is not the same at all the levels of the other factor.
There are three main types of interactions:
When there is a large interaction, main effects have little practical meaning as a significant interaction often masks the significance of main effects.
There are three main types of factorial designs, namely “Within Subject Factorial Design”, “Between Subject Factorial Design”, and “Mixed Factorial Design”.
The following are a few advantages of using the factorial experimental design:
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A factorial experimental design is an experimental design that is used to study two or more factors, each with multiple discrete possible values or “levels”.
When compared to the one-factor-at-a-time design (OFAT), factorial designs are less expensive, more efficient, and produce more comprehensive results.
The main effect of a factor can be defined as the change produced as a result of a change in the level of the factor.
When the difference in response between the levels of one factor is not the same at all the levels of the other factor, there is an interaction between the factors.
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