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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.

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...

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

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...

Data Validation

Data Validation

Method validation is a crucial process in analytical chemistry designed to confirm that a given method consistently produces reliable and high-quality results. This process is essential when a method is applied to different sample matrices or when procedural modifications are made, ensuring that the results meet acceptable standards across various applications.
Key parameters for method validation include:

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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A heteroscedastic measurement error model for method comparison data with replicate measurements.

Lakshika S Nawarathna¹, Pankaj K Choudhary

¹Department of Statistics and Computer Science, University of Peradeniya, Peradeniya 20400, Sri Lanka.

Statistics in Medicine

|January 24, 2015

Summary

This summary is machine-generated.

This study introduces a new heteroscedastic measurement error model for comparing quantitative measurement methods. The model handles non-linear relationships and varying error, improving analysis of real-world data like cholesterol measurements.

Keywords:

agreement calibration mixed-effects model nonlinear model repeated measures total deviation index

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Area of Science:

Biostatistics
Measurement Science
Statistical Modeling

Background:

Measurement error models are crucial for comparing quantitative measurement methods.
Standard models often assume homoscedasticity and linear relationships, which may not hold true.
Violations necessitate advanced models, such as heteroscedastic measurement error models.

Purpose of the Study:

To present a novel heteroscedastic measurement error model for replicated measurements.
To address nonlinear relationships and heteroscedasticity in measurement data.
To provide methods for evaluating method similarity and agreement.

Main Methods:

Development of a heteroscedastic measurement error model allowing nonlinear true value relationships.
Exploration of model fitting techniques using approximate maximum likelihood estimation.
Evaluation of fitting methods through a simulation study.

Main Results:

The proposed model effectively accommodates heteroscedasticity and nonlinearities in measurement data.
Approximate maximum likelihood estimation provides viable solutions for model fitting.
The methodology was successfully applied to a cholesterol dataset.

Conclusions:

The developed heteroscedastic measurement error model offers a flexible framework for complex measurement comparison studies.
The proposed fitting and evaluation methods are robust and applicable to real-world data.
This approach enhances the accuracy of assessing measurement method agreement and similarity.