Definition and assessment of sampling and analytical accuracy

Area of Science:

• Metrology and Measurement Science
• Statistical Analysis
• Quantitative Research Methods

Background:

• Accurate measurement is critical in scientific and industrial applications.
• Quantifying measurement accuracy requires robust statistical methods to account for various error sources.
• Existing methods for assessing accuracy may differ in their approach and interpretation.

Purpose of the Study:

• To compare two independent definitions of measurement accuracy: Gauss' mean square error (MSE) and symmetric-range accuracy (A).
• To evaluate two distinct schemes for assessing these accuracy measures.
• To present methods for computing confidence limits on measurement accuracy, considering different evaluation strategies.

Main Methods:

• Comparative analysis of Gauss' mean square error (MSE) and symmetric-range accuracy (A).
• Application of statistical theories, including tolerance intervals and confidence intervals.
• Examination of accuracy assessment schemes under initial versus continual method evaluation.

Main Results:

• Gauss' MSE and symmetric-range accuracy (A) are found to be closely equivalent for most applications.
• Systematic error (bias) and imprecision are accounted for in both accuracy measures.
• Confidence limits on measurement accuracy differ qualitatively based on whether method evaluation is initial or continual.

Conclusions:

• The equivalence of MSE and symmetric-range accuracy simplifies the choice of accuracy metrics in many scenarios.
• Accurate calculation of confidence limits is essential for reliable method evaluation.
• Statistical theories provide a framework for understanding and quantifying measurement uncertainty and accuracy.