A general minimum lower-order confounding criterion for s-level blocked designs

Zhi Li and Zhi-Ming Li

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 5, 1410-1426

Abstract: Blocked designs are widely used in practical experiments with heterogeneous experimental units. The blocked general minimum lower-order confounding (B1-GMC) criterion is appropriate for selecting optimal blocked designs. This article extends B1-GMC criterion to s-level blocked designs. First, we introduce a blocked aliased component-number pattern (B1-ACNP) to reflect the confounding information among various component effects s. Further, the existing optimal criteria can be expressed by some functions of elements in the B1-ACNP. Finally, we not only give the formulas of lower-order confounding information by the complementary method, but also provide an algorithm to calculate the lower-order confounding in blocked designs. Some examples are given to illustrate our theoretical results.

Date: 2025
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DOI: 10.1080/03610926.2024.2340598

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