by Hening Huang
This paper further explores the t-interval method and the mean-unbiased estimator for uncertainty estimation with a small number of measurements. It describes the logic behind the error bound-based definition of uncertainty, which leads to the mean-unbiased estimator. To reflect the physical meaning of an interval, we suggest using the term ‘degree of certainty’ for the probability associated with a probability interval (e.g. the z-interval) and ‘capture rate’ for the probability associated with a confidence interval (e.g. the t-interval). We propose a physical law-based criterion for validating uncertainty estimation methods. Results from detailed error and uncertainty analyses for a dataset of Mississippi River discharge measurements are presented as an example to demonstrate the appropriateness of the mean-unbiased estimator and the inappropriateness of the t-interval method for measurement uncertainty estimation. Read Full Article (PDF)
