Biometrical Letters Vol. 53(2), 2016, pp. 119-131
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A NOTE ON THE D-OPTIMALITY AND D-EFFICIENCY OF NONORTHOGONAL BLOCKED MAIN EFFECTS PLANS Łukasz Smaga Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland, e-mail: ls@amu.edu.pl |
This paper considers main effects plans used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. The assumptions are adopted that n ≡ 2 (mod 8) and k > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by Jacroux (2011a) to be D-optimal when (m - 2)(k - 2) + 2 ≤ n ≤ (m - 1)(k - 2) + 2. Here, we extend that result. For (m - 3)(k - 2) + 2 ≤ n < (m - 2)(k - 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(m + 1) ≤ n < (m - 3)(k - 2) + 2, indicating their good performance under the criterion of D-optimality.
blocked main effects plan, D-efficiency; D-optimality, Fischer’s inequality, Hadamard’s inequality, nonorthogonality
