Reporting measurement uncertainty and coverage intervals near natural limits

Area of Science:

• Statistics
• Analytical Chemistry
• Data Analysis

Background:

• Scientific data often falls within natural limits (e.g., 0% or 100% fractions).
• Standard statistical methods may produce results outside these feasible ranges.
• Accurate data treatment near limits is crucial for reliable scientific conclusions.

Purpose of the Study:

• To evaluate various methods for treating data near natural limits.
• To recommend the most appropriate statistical approach for such data.
• To ensure the integrity and interpretability of scientific measurements.

Main Methods:

• Discussion of data treatment techniques: discarding, shifting, interval truncation, and Bayesian estimation.
• Simulation studies to assess bias and coverage probability of different methods.
• Comparison of classical confidence intervals (Student's t) with Bayesian approaches.

Main Results:

• Truncating classical confidence intervals (Student's t) is recommended for most applications.
• Adjusting results to remain within the feasible range is advised when necessary.
• Retaining original standard uncertainty is suggested for subsequent propagation calculations.

Conclusions:

• A practical, robust method for constructing confidence intervals near natural limits is proposed.
• The recommended method balances statistical rigor with practical applicability.
• This approach enhances the reliability of data analysis in fields with bounded variables.