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Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

Random and Systematic Errors

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

Random and Systematic Errors

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Systematic Error: Methodological and Sampling Errors

Systematic Error: Methodological and Sampling Errors

In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...

Statistical Analysis: Overview

Statistical Analysis: Overview

When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...

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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Uncertainties of method performance statistics based on a balanced completely randomized model interlaboratory study.

Foster D McClure¹, Jung K Lee

¹U.S. Food and Drug Administration, Center for Food Safety and Applied Nutrition, Communication and Emergency Response, Division of Public Health and Biostatistics, Biostatistics Branch, College Park, MD 20740-3835, USA. fdmc5100@yahoo.com

Journal of AOAC International

|June 24, 2008

Summary

This study introduces formulas for calculating population variances and uncertainties for analytical method performance statistics. These formulas provide unbiased estimates for sample mean, repeatability, and reproducibility variances and standard deviations.

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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Published on: January 23, 2018

Area of Science:

Analytical Chemistry
Statistical Methods

Background:

Method performance statistics are crucial for analytical method validation.
Accurate estimation of variances and uncertainties is essential for reliable results.

Purpose of the Study:

To develop formulas for deriving population variances and uncertainties for key method performance statistics.
To provide unbiased estimates for sample mean, repeatability, and reproducibility.

Main Methods:

Utilized exact and asymptotic distributions.
Derived formulas for population variances and uncertainties.
Applied formulas to collaborative study data.

Main Results:

Formulas were developed for unbiased estimation of sample mean (y..).
Formulas provide unbiased estimates for repeatability variance (s2r) and standard deviation (sr).
Formulas yield unbiased estimates for reproducibility variance (s2R) and standard deviation (sR).

Conclusions:

The developed formulas enable accurate derivation of population variances and uncertainties.
These methods enhance the reliability of performance statistics from collaborative analytical studies.