Coding of factorial designs

Calculations for factorial designs are often greatly simplified if coding of factor levels is employed (see Section 8.5). For the present example, setting c,i = c = 5 

Transformation back to the original coordinate system is accomplished as described in Section 11.5. 

Many workers do not transform the parameter estimates back to the original coordinate system, but instead work with the parameter estimates obtained in the coded factor space. This can often lead to surprising and seemingly contradictory results. As an example, the fitted model in the coded factor space was found to be 

This suggests that the PJ term can be omitted and leads to a simpler model of the form 

it is the algebraic effect of coding and the numerical values of the estimated parameters that cause some terms to be added to the model (e.g., P2) and other terms to disappear from the model (e.g., P,). Transformation of parameter estimates back to the original factor space usually avoids possible misinterpretation of results. 

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