This article is about factorial design. For factor full factorial design of experiments pdf, see Factor analysis.
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. Factorial designs were used in the 19th century by John Bennet Lawes and Joseph Henry Gilbert of the Rothamsted Experimental Station.
No aphorism is more frequently repeated in connection with field trials, than that we must ask Nature few questions, or, ideally, one question, at a time. The writer is convinced that this view is wholly mistaken.
Nature, he suggests, will best respond to “a logical and carefully thought out questionnaire”. A factorial design allows the effect of several factors and even interactions between them to be determined with the same number of trials as are necessary to determine any one of the effects by itself with the same degree of accuracy. Frank Yates made significant contributions, particularly in the analysis of designs, by the Yates analysis.
The term “factorial” may not have been used in print before 1935, when Fisher used it in his book The Design of Experiments. Many experiments examine the effect of only a single factor or variable. Factorial designs are more efficient than OFAT experiments.
They provide more information at similar or lower cost. They can find optimal conditions faster than OFAT experiments. Factorial designs allow additional factors to be examined at no additional cost.
When the effect of one factor is different for different levels of another factor, it cannot be detected by a OFAT experiment design. Factorial designs are required to detect such interactions. Use of OFAT when interactions are present can lead to serious misunderstanding of how the response changes with the factors.
Factorial designs allow the effects of a factor to be estimated at several levels of the other factors, yielding conclusions that are valid over a range of experimental conditions. In his book, “Improving Almost Anything”, the famous statistician George Box gives many examples of the benefits of factorial experiments. Engineers at the bearing manufacturer SKF wanted to know if changing to a less expensive “cage” design would affect bearing life. The engineers asked Christer Hellstrand, a statistician, for help in designing the experiment .