Group orthogonal supersaturated designs (GOSSD) are constructed to have a specific structure to facilitate model selection. The design factors are partitioned into groups such that factors within a group are correlated with other factors within the same group yet factors are orthogonal to factors in other groups. One group consists of three or more “fake” factors. These fake factors are not assigned to design factors. They are used only in the analysis of the design. The fake factors provide an unbiased estimate of the variance assuming that second-order and higher-order effects are negligible.
Practical considerations for setting up a GOSSD include:
• More groups are better than fewer groups.
• Factors that are thought to be active should be placed in separate groups.
• Choose the levels of factors so that anticipated coefficients are positive.