A note on experimental design

The parameters in the response surface model will allow for an evaluation of each variable if the estimated value of each model parameter is independent of the estimated value of other model parameters. (For certain experimental designs, this is not possible to attain, but the estimates are as independent as possible.) 

The parameters should measure the influence of the corresponding variables, i.e. the slopes of the surface, flj, as measures of linear dependencies of the variables the twists of the surface, By, as measures of interactions between variables, and the curvatures, fly, as measures or non-linear influences of the variables, and nothing else This calls for careful spacing of the variable settings in the experimental domain to determine the series of experiments used to estimate the parameters, i.e. the experimental design. These aspects will be treated in detail in the following chapters Chapters 5-7, which deal with screening experiments based on linear and second order interaction models, and Chapter 12, which describes quadratic models for optimization. 

2 This is according to the principle of Occham s razor, which says that if there are several possible explanations, we should choose the most simple one. 

---