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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...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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Related Experiment Video

Updated: Dec 29, 2025

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

High-efficiency sub-microscale uncertainty measurement method using pattern recognition.

Chenyang Zhao¹, Chi Fai Cheung², Peng Xu³

¹School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen 518055, China; State Key Laboratory of Ultra-precision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China.

ISA Transactions

|February 11, 2020

Summary

This summary is machine-generated.

This study introduces a fast precision measurement technique using pattern recognition. The novel method achieves 90-nm length uncertainty and speeds up measurements 1000x.

Keywords:

Image processing Neural network Polar microstructure Precision measurement

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Last Updated: Dec 29, 2025

Picometer-Precision Atomic Position Tracking through Electron Microscopy

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Published on: July 3, 2021

Atomically Traceable Nanostructure Fabrication

Atomically Traceable Nanostructure Fabrication

Published on: July 17, 2015

Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles

Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles

Published on: March 13, 2017

Area of Science:

Metrology
Optical Engineering
Computer Vision

Background:

Precision measurement is crucial in various scientific and industrial fields.
Existing methods can be slow or lack the required accuracy for micro-scale applications.

Purpose of the Study:

To develop a fast and accurate precision measurement method using pattern recognition.
To enhance measurement speed and reduce uncertainty at the micro-scale.

Main Methods:

Design and manufacture of a micro-structured surface with a unique pattern.
Development of a measurement system integrating circle Hough transform (CHT), neural classifier (NC), template matching (TM), and sub-pixel interpolation (SI).
Experimental validation focusing on circle detection, length uncertainty, and measurement speed.

Main Results:

Achieved over 96% correct circle classification.
Circle Hough transform (CHT) search accuracy within a two-pixel level.
Demonstrated 90-nm length uncertainty.
Increased measurement speed by a factor of 1000 compared to the original method.

Conclusions:

The proposed pattern recognition method significantly enhances measurement speed and precision.
The integration of advanced algorithms (CHT, NC, TM, SI) enables high-accuracy micro-scale measurements.
This technique offers a viable solution for demanding metrology applications.