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In this paper, we study saturated two-level main effects designs which are commonly used for screening experiments. The QB criterion, which incorporates experimenters' prior beliefs about the probability of factors being active is used to compare designs. We show that under priors with more weight on models of small size, p-effcient designs should be recommended; when models with more parameters are of interest, A-optimal designs would be better. We identify new classes of saturated main effects designs between these two designs under different priors. The way in which the choice of designs depends on experimenters' prior beliefs will be demonstrated for the cases when the number of runs N = 2 mod 4. A novel method of construction of QB-optimal designs using conference matrices is introduced. Complete families of optimal designs are given for N = 6; 10; 14; 18; 26; 30

New families of Q_B-optimal saturated two-level main effects screening designs