Isolation of degrees of freedom for box—behnken designs

The Box–Behnken three-level designs have proved useful for fitting second-order response surfaces to experimental data. Here, we discuss an aspect of their value in the detection of lack of model fit. The degrees of freedom in excess of those needed to fit the model can be used advantageously for contrasts which estimate certain higher-order departures from the model. These can be expressed in various forms. Some forms, in which these contrasts are orthogonal, permit the plotting of the contrasts in a normal plot for easy detection of model bias.