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Chapter 18. Elements of Experimental Des... > Multi-factor Experiments and Factori...

Multi-factor Experiments and Factorial Designs

It might be natural to think that one should experiment by holding all factors constant except for one, and systematically alter the values or levels of that single factor. So, for example, we might want to test varying amounts of sand in concrete mixtures with all other components being held at given quantities. The shortcoming of such an approach is that it can conceal an important combined influence of two or more factors. Perhaps the sand quantity is not nearly as important as the ratio of sand to coarser aggregate. When two variables combine to lead to a result, we say that there is an interaction between the two, and if, in reality, there is an important interaction to be found, we'll never find it by examining only one factor or the other. We need to vary multiple factors at a time.

Another way to conceive of the issue is in terms of a three-dimensional response surface. Imagine that we have a response variable and two factors. If both factors were to contribute to the response in a simple additive and linear fashion (more of component A increases strength, more of component B weakens strength) then it would not matter if we vary A and B individually or jointly. The response variable would vary by strictly increasing one direction and decreasing in the other. The three variables together would form a plane, and by varying A and then B, we'd essentially be sliding up or down the plane in one direction or the other.


  

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