Assessing the Impact of Measurement Uncertainty on Statistical Inference and Confidence Interval Accuracy

Posted: Oct 07, 2025

• Mason Wright
• Logan Hill
• Jack Roberts

Abstract

Statistical inference forms the bedrock of scientific research, providing the framework through which we draw conclusions from data. Central to this framework is the concept of confidence intervals, which quantify the uncertainty in parameter estimates and facilitate hypothesis testing. The theoretical foundation of confidence intervals, as developed by Neyman and Pearson, relies on the assumption that measurements are exact representations of the underlying phenomena. However, this assumption is fundamentally flawed in virtually all real-world applications. Measurement instruments have finite precision, human observers introduce variability, and environmental conditions introduce noise. The conventional approach to handling measurement error has been either to ignore it entirely or to treat it as a secondary concern addressed through sensitivity analyses. This research challenges this paradigm by demonstrating that measurement uncertainty is not merely a nuisance but a fundamental component that must be integrated directly into the inferential process. Our investigation reveals that the impact of measurement uncertainty on confidence interval accuracy is both substantial and systematically misunderstood. When measurements contain error, the sampling distribution of statistics changes in ways that conventional methods fail to capture. This leads to confidence intervals that do not achieve their nominal coverage probabilities, potentially invalidating scientific conclusions. The problem is particularly acute in fields where measurement precision is inherently limited, such as psychology, ecology, economics, and medical diagnostics. Despite its importance, the literature contains surprisingly few comprehensive treatments of how measurement uncertainty propagates through the entire inferential chain.