Factorial versus one-at-a-time design

An experiment such as the one in the previous example, where the response variable (i.e. the molar absorptivity) is measured for all possible combinations of the chosen factor levels, is known as a complete factorial design. The reader may have noticed that this design of the experiment is the antithesis of the classical approach in which the response is investigated for each factor in turn while all the other factors are held at a constant level. There are two reasons for preferring a factorial design to a classical design in experiments that test whether the response depends on factor level  

1 The factorial experiment detects and estimates any interaction, which the one-at-a-time experiment cannot. 

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