The Logical Limits of Bias Analysis in Scientific Inquiry

Bias analysis is widely discussed in statistics as the expected deviation of an estimator from the true parameter, commonly expressed as Bias(θ ̂ )=E[θ ̂ ]-θ. While mathematically rigorous within fully specified models, this definition becomes logically problematic in empirical science, where θ represents truth and is precisely the quantity under investigation. This short article clarifies why traditional bias analysis cannot meaningfully quantify reality, distinguishes it from legitimate sensitivity analysis, and situates it appropriately within the broader framework of scientific reasoning.