ABSTRACT
III. Analysis of variance (ANOVA) Example of a single factor Analysis of variance for the replicated 22 full factorial design with centre points Statistical significance of the coefficients Replication of a factorial design
IV. Quality of a design Statistical criteria for design quality Applications to various designs
I. INTRODUCTION
Whether it is to understand or interpret a phenomenon, as in the factor study (chapter 3), or to predict results under different conditions by response surface modelling (as we will see in the next chapter), we require a mathematical model that is close enough in its behaviour to that of the real system. The models we use are polynomials of coded (normalised) variables, representing factors that are all transformed to the same scale and with constant coefficients. It is the unknown value of each coefficient that must be estimated with the best possible precision by experiments whose position in the experimental factor space is chosen according to the form of the mathematical model postulated. For this to be possible, the number of distinct experiments (that is not counting replications) must be at least equal to the number of coefficients in the model.
