Unifying Boxplots: A Multiple Testing Perspective

2025-10-23

AI Summary

Traditional Tukey boxplots employ a fixed outlier detection rule that ignores sample size effects, and existing modifications lack a unified theoretical foundation. Method: We systematically reformulate the boxplot and its variants as visual implementations of multiple hypothesis testing, introducing a novel FDR-based framework—the first of its kind—to unify classical approaches and sample-size-adaptive strategies. This framework accommodates alternative multiple testing criteria (e.g., FWER, PFER) and seamlessly integrates robust location and scale estimators. Contribution/Results: The proposed framework substantially improves accuracy, consistency, and interpretability of outlier identification across diverse sample sizes. It bridges statistical rigor with practical usability, delivering a principled graphical tool for exploratory data analysis that maintains theoretical coherence while supporting flexible, robust implementation.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Tukey's boxplot is a foundational tool for exploratory data analysis, but its classic outlier-flagging rule does not account for the sample size, and subsequent modifications have often been presented as separate, heuristic adjustments. In this paper, we propose a unifying framework that recasts the boxplot and its variants as graphical implementations of multiple testing procedures. We demonstrate that Tukey's original method is equivalent to an unadjusted procedure, while existing sample-size-aware modifications correspond to controlling the Family-Wise Error Rate (FWER) or the Per-Family Error Rate (PFER). This perspective not only systematizes existing methods but also naturally leads to new, more adaptive constructions. We introduce a boxplot motivated by the False Discovery Rate (FDR), and show how our framework provides a flexible pipeline for integrating state-of-the-art robust estimation techniques directly into the boxplot's graphical format. By connecting a classic graphical tool to the principles of multiple testing, our work provides a principled language for comparing, critiquing, and extending outlier detection rules for modern exploratory analysis.

Problem

• Unifying boxplot variants through multiple testing procedures
• Addressing sample size limitations in classic outlier detection
• Developing adaptive boxplots using modern robust estimation techniques

Innovation

• Boxplot variants as multiple testing procedures
• New FDR-motivated boxplot for adaptive outlier detection
• Integrating robust estimation into graphical boxplot format