Confounding analysis of s-level designs with multi-block variables

2026-06-23

AI Summary

This study addresses the confounding problem in s-level factorial designs with multiple blocking factors by proposing a new confounding metric, termed the Blocked Aliasing Component Number Pattern (B²-ACNP). Built upon the block word-length distribution matrix, B²-ACNP provides a unified characterization of the classification structures underlying existing design criteria. The work introduces an accompanying algorithm and visualization tools to systematically analyze complex confounding relationships across multiple blocks. A comprehensive evaluation framework is established that generalizes and integrates classical design criteria. Implemented in Python and validated through illustrative examples, the proposed B²-ACNP demonstrates both effectiveness and practical utility in comparing and assessing the confounding properties of s-level multi-block designs.

Abstract

In practical experiments, block variables often arise from multiple sources of heterogeneity. To address the confounding problem, this paper proposes a blocked aliased component-number pattern (B$^2$-ACNP) to analyze the confounding properties of s-level designs with multi-block variables. We calculate the values of (B$^2$-ACNP) via a blocked wordlength distribution matrix. The classification patterns of existing criteria can be expressed as functions of specific elements within the B$^2$-ACNP, thereby stablishing connections within a unified framework. Further, we provide confounding algorithms and visualization methods of the B$^2$-ACNP. Finally, case analysis clarifies the significant role of the B$^2$-ACNP. The Python code is available in the Appendix.

Problem

• confounding
• s-level designs
• multi-block variables
• blocked designs
• experimental design

Innovation

• B²-ACNP
• multi-block variables
• confounding analysis
• s-level designs
• blocked wordlength distribution