APCanalysis: an R package for identifying active factors using the APC method

Abu Zar Md. Shafiullah and Arden Miller

Journal of Applied Statistics, 2026, vol. 53, issue 5, 937-957

Abstract: Unreplicated two-level designs play an important role in screening experiments. Notably, Plackett–Burman designs (PBDs) and regular fractional factorial designs ( $ 2^{k-p} $ 2k−p) are commonly used for their flexible run sizes and orthogonal contrasts. However, classical methods such as t-tests are not applicable for identifying significant effects in saturated models due to insufficient degrees of freedom. The All Possible Comparisons (APC) method addresses this limitation by providing an objective framework to control false positive rates, specifically the individual error rate (IER) and the experiment-wise error rate (EER). In this article, we introduce APCanalysis, a user-friendly R package that implements the APC method using a tailored AIC-type model selection criterion, the APC-criterion. The package features an advanced penalty algorithm extending error control to the false discovery rate (FDR). It supports main effects screening in PBDs, active main effects and interactions in full factorial ( $ 2^k $ 2k) and resolution-V ( $ 2^{k-p}_V $ 2Vk−p) designs, and detects active alias strings in resolution-IV ( $ 2^{k-p}_{IV} $ 2IVk−p) and resolution-III ( $ 2^{k-p}_{III} $ 2IIIk−p) designs. Through examples, simulations, and real-world data, we demonstrate that the APC-criterion reliably identifies active factors while maintaining user-specified error thresholds for IER, EER, or FDR. Benchmarking against Lenth's method in a validation study further confirms strong agreement in screening power and accuracy. This article provides practical guidance on applying APCanalysis, highlighting its advantages and limitations. The package is available via the Comprehensive R Archive Network (CRAN).

Date: 2026
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DOI: 10.1080/02664763.2025.2540378

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