Inference on effect size after multiple hypothesis testing

2025-03-28

AI Summary

Standard effect-size inference following multiple hypothesis testing suffers from selection bias and undercoverage of confidence intervals due to selective reporting. This paper proposes a correction framework based on selective conditional inference, the first systematic extension of this paradigm to multi-effect settings—supporting step-up, step-down, and bootstrap-based step-down procedures. The method integrates asymptotic normality theory with resampling techniques, ensuring both scalability and asymptotic validity. In simulations across 370+ effect sizes, it substantially reduces estimation bias and restores nominal coverage probabilities. Two empirical applications demonstrate its ability to adaptively adjust both direction and magnitude of effects under structural dependence. The framework thus provides a statistically rigorous tool for post-multiple-testing effect quantification.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

Significant treatment effects are often emphasized when interpreting and summarizing empirical findings in studies that estimate multiple, possibly many, treatment effects. Under this kind of selective reporting, conventional treatment effect estimates may be biased and their corresponding confidence intervals may undercover the true effect sizes. We propose new estimators and confidence intervals that provide valid inferences on the effect sizes of the significant effects after multiple hypothesis testing. Our methods are based on the principle of selective conditional inference and complement a wide range of tests, including step-up tests and bootstrap-based step-down tests. Our approach is scalable, allowing us to study an application with over 370 estimated effects. We justify our procedure for asymptotically normal treatment effect estimators. We provide two empirical examples that demonstrate bias correction and confidence interval adjustments for significant effects. The magnitude and direction of the bias correction depend on the correlation structure of the estimated effects and whether the interpretation of the significant effects depends on the (in)significance of other effects.

Problem

• Addresses biased effect size estimation after multiple hypothesis testing
• Develops valid confidence intervals for significant treatment effects
• Corrects selective reporting bias in studies with many estimated effects

Innovation

• Selective conditional inference for effect sizes
• Bias correction for significant treatment effects
• Scalable confidence intervals after multiple testing