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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.

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.

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

NMR Spectrometers: Resolution and Error Correction

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

Uncertainty in Measurement: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

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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

Published on: September 7, 2019

Uncertainty Due to Finite Resolution Measurements.

S D Phillips¹, B Toman¹, W T Estler¹

¹National Institute of Standards and Technology, Gaithersburg, MD 20899.

Journal of Research of the National Institute of Standards and Technology

|April 21, 2016

Summary

This summary is machine-generated.

Finite resolution significantly impacts measurement uncertainty, especially with Gaussian noise. A direct relationship between standard deviation and confidence-level uncertainty is absent, though mean and standard deviation are analytically linked.

Keywords:

ISO 14253-2 Sheppard’s correction digitization measurement resolution standard deviation uncertainty

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Area of Science:

Metrology
Measurement Science
Data Analysis

Background:

The Guide to the Expression of Uncertainty in Measurement (GUM) provides a framework for quantifying measurement uncertainty.
Finite resolution is a common factor in measurements that can introduce systematic effects.
Discrepancies exist between GUM and other standards like ISO 14253-2 regarding finite resolution uncertainty.

Purpose of the Study:

To analyze the impact of finite resolution on measurement uncertainty.
To evaluate the GUM's approach to finite resolution uncertainty.
To compare GUM with ISO 14253-2 for finite resolution uncertainty evaluation.

Main Methods:

Investigated measurement results distribution under Gaussian noise with finite resolution.
Analyzed the relationship between the true value and resolution increment.
Derived analytic relations between mean and standard deviation of measurement results.
Compared GUM and ISO 14253-2 methods for standard uncertainty evaluation.

Main Results:

Measurement result distribution strongly depends on the true value's position relative to the resolution increment.
No simple expression directly links standard deviation to uncertainty at a specific confidence level.
An analytic relation exists between the mean and standard deviation of measurement results.
The GUM method is generally superior to ISO 14253-2 on average but remains an approximation.

Conclusions:

Finite resolution introduces complexity in uncertainty evaluation not fully captured by simple GUM expressions.
The GUM's approach to finite resolution uncertainty is an approximation, necessitating careful application.
Further research may be needed to refine uncertainty evaluation methods for finite resolution effects.