Causal Inference in Counterbalanced Within-Subjects Designs

2025-05-06

AI Summary

Counterbalanced within-subject experiments risk invalid causal inference due to unverifiable and often violated assumptions—particularly the symmetry and cancelability of carryover effects. Method: We introduce “sequential exchangeability” as a formal identification assumption within the potential outcomes framework, rigorously exposing inherent limitations of counterbalancing; we then develop actionable strategies—including diagnostic tests, optimized washout periods, covariate adjustment, and alternative sequence designs—grounded in causal identification theory, sequential randomization modeling, and sensitivity analysis. Contribution/Results: Our work delineates precise validity boundaries for counterbalanced designs, providing rigorous, practical guidelines for within-subject experimentation in psychology, human-computer interaction, and related fields. By addressing foundational identifiability concerns, it substantially enhances the reliability of causal inference in repeated-measures settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Experimental designs are fundamental for estimating causal effects. In some fields, within-subjects designs, which expose participants to both control and treatment at different time periods, are used to address practical and logistical concerns. Counterbalancing, a common technique in within-subjects designs, aims to remove carryover effects by randomizing treatment sequences. Despite its appeal, counterbalancing relies on the assumption that carryover effects are symmetric and cancel out, which is often unverifiable a priori. In this paper, we formalize the challenges of counterbalanced within-subjects designs using the potential outcomes framework. We introduce sequential exchangeability as an additional identification assumption necessary for valid causal inference in these designs. To address identification concerns, we propose diagnostic checks, the use of washout periods, and covariate adjustments, and alternative experimental designs to counterbalanced within-subjects design. Our findings demonstrate the limitations of counterbalancing and provide guidance on when and how within-subjects designs can be appropriately used for causal inference.

Problem

• Challenges in causal inference with counterbalanced within-subjects designs
• Unverifiable assumptions about symmetric carryover effects in counterbalancing
• Need for alternative methods to ensure valid causal inference

Innovation

• Introduces sequential exchangeability for causal inference
• Proposes diagnostic checks and washout periods
• Suggests alternative designs to counterbalancing