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Uncertainty in Measurement: Reading Instruments

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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...

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Related Experiment Video

Updated: Jun 10, 2026

Software-Assisted Quantitative Measurement of Osteoarthritic Subchondral Bone Thickness

Software-Assisted Quantitative Measurement of Osteoarthritic Subchondral Bone Thickness

Published on: March 18, 2022

Comparison of measurements by multiple methods or instruments.

Douglas M Hawkins¹, Abha Sharma

¹School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, USA. dhawkins@umn.edu

Journal of Biopharmaceutical Statistics

|August 20, 2010

Summary

Comparing multiple devices is complex. This study introduces a hierarchical modeling framework to analyze bias and variance across three or more measurement devices, improving accuracy in comparative studies.

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

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Last Updated: Jun 10, 2026

Software-Assisted Quantitative Measurement of Osteoarthritic Subchondral Bone Thickness

Software-Assisted Quantitative Measurement of Osteoarthritic Subchondral Bone Thickness

Published on: March 18, 2022

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

Area of Science:

Analytical Chemistry
Statistical Modeling
Biostatistics

Background:

Traditional device comparison methods often focus on pairwise analyses.
Existing models primarily address constant bias or linear relationships with true values.
Comparing three or more devices presents unique statistical challenges not fully addressed by current methods.

Purpose of the Study:

To develop a hierarchical modeling framework for comparing three or more measurement devices.
To extend existing models by incorporating multiplicative interaction terms.
To provide a robust method for analyzing complex bias and variance structures in multi-device comparisons.

Main Methods:

Development of a hierarchical statistical model.
Inclusion of multiplicative interaction terms to capture complex relationships.
Application of the model to settings with varying analyte concentrations and measurement variances.

Main Results:

The proposed hierarchical models effectively capture departures from simple bias or linear relationships.
Multiplicative interaction terms can identify outliers and differing measurement variances between devices.
The framework provides a more comprehensive understanding of device performance compared to traditional methods.

Conclusions:

The hierarchical modeling approach offers a significant advancement for comparing multiple measurement devices.
This method enhances the ability to detect subtle differences and systematic errors across devices.
The framework is applicable to various fields requiring accurate multi-device performance evaluation.