Centered experimental designs and coding

Another, often major, advantage of using coded factor levels is that the numerical values involved in matrix manipulations are smaller (especially the products and sums of products), and therefore are simpler to handle and do not suffer as much from round-off errors. 

It is to be stressed, however, that the geometric interpretation of the parameter estimates obtained using coded factor levels is usually different from the interpretation of those parameter estimates obtained using uncoded factor levels. As an illustration, pj (the intercept in the coded system) represents the response at the center of the experimental design, whereas Pq (the intercept in the uncoded system) represents the response at the origin of the original coordinate system the two estimates (Pq and Pq) are usually quite different numerically. This difficulty will not be important in the remainder of this book, and we will feel equally free to use either coded or uncoded factor levels as the examples require. Later, in Section 11.5, we will show how to translate coded parameter estimates back into uncoded parameter estimates. 

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