Secondary Criteria in the Selection of Minimum Bias Designs in Two Variables

For the second order estimating function, ŷ(x), and third order true function η(x) in two variables, secondary criteria are used to select a design from the class of average minimum bias designs. It is shown that designs can be constructed which not only allow estimation of a cubic model with nearly minimum variance averaged over a square but also provide for efficient lack of fit tests. Average qiradratic variance is also evaluated. Specific 12 point and 16 point designs are recommended.