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

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.