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History

Factorial designs were used in the 19th century by John Bennet Lawes and Joseph Henry Gilbert of the Rothamsted Experimental Station.

Ronald Fisher argued in 1926 that "complex" designs (such as factorial designs) were more efficient than studying one factor at a time. Fisher wrote,

"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; indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed."

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.