Factorial Experiment
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A Factorial Experiment is an experiment designed to investigate the effect of two or more factors .
References
2015
- (Wikipedia, 2015) ⇒ https://www.wikiwand.com/en/Factorial_experiment
- 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. 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.
If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.
- 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. 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.
2008
- (Upton & Cook, 2008).
- Factorial Design; Factorial Experiment: An *experimental design to investigate the effects of several explanatory variables, in this context called factors, on a single response variable. Each factor takes only a small number of different values (typically two), which may not be quantitative and are called levels. For example, in an agricultural context the two levels might be two different varieties of a plant. Sir Ronald Fisher introduced the term 'factor' in 1929 and used the description ‘factorial design' as a chapter heading in his seminal work The Design of Experiments, published in 1935.
- An experiment with [math]\displaystyle{ k }[/math]k two-level factors (the upper and lower levels) is called a [math]\displaystyle{ 2^k }[/math]-factorial. The standard notation denotes factors by capital letters [math]\displaystyle{ A, B, ... }[/math]. Each experimental unit is subject to one or other of the levels of each factor. Lower-case letters are used to indicate factor combinations, so [math]\displaystyle{ ac }[/math] indicates that [math]\displaystyle{ A }[/math] and [math]\displaystyle{ C }[/math] occur at the higher level for that experimental unit, a.nd other factors occur at tfre lower level. The combination with all factors at the lower level is indicated as (1), so the eight treatment combinations for a [math]\displaystyle{ 2^3 }[/math]-factorial are
- [math]\displaystyle{ \begin{matrix} (1) & a & b & ab & c & ac & bc & abc.\\ \end{matrix} }[/math]
- A [math]\displaystyle{ 2^3 }[/math]-factorial enables one to estimate the three main effects (see below) as well as the three *interactions involving two variables and the three-variable interaction. The main effect ofA compares the mean value of the observations at the higher level (a, ab, ac, bc), for example, with those at the lower level [math]\displaystyle{ ( (1) b, c, bc). }[/math]