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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.

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...

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

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...

Margin of Error

Margin of Error

The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.

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Related Experiment Video

Updated: Jul 2, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Ratio estimation with measurement error in the auxiliary variate.

Timothy G Gregoire¹, Christian Salas

¹School of Forestry and Environmental Studies, Yale University, New Haven, Connecticut 06511-2104, USA. timothy.gregoire@yale.edu

|September 2, 2008

Summary

Ratio estimation using auxiliary information enhances efficiency. However, measurement error in auxiliary variates can impact ratio estimators, with the ratio-of-means estimator showing notable resistance to such errors.

Related Experiment Videos

Last Updated: Jul 2, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Statistics
Survey Methodology
Statistical Inference

Background:

Ratio estimation is a powerful technique for finite population total estimation when auxiliary information is available.
Measurement error in auxiliary variables can significantly distort the properties of standard ratio estimators.
Understanding these distortions is crucial for reliable statistical inference in surveys.

Purpose of the Study:

To investigate the impact of measurement error in auxiliary variates on the design-based properties of three common ratio estimators.
To analyze both systematic and variable measurement error effects.
To provide a comparative assessment of estimator performance under measurement error conditions.

Main Methods:

Mathematical derivation of bias and variance expressions for ratio estimators under measurement error.
Numerical analysis using a specific population dataset.
Examination of systematic and variable measurement error scenarios.

Main Results:

Systematic measurement error introduces asymmetric bias; precision can be enhanced or diminished based on error magnitude.
Variable measurement error increases bias in the ratio-of-means estimator less than in the mean-of-ratios estimator.
The mean-of-ratios estimator exhibits greater precision loss under variable measurement error compared to other examined estimators.

Conclusions:

The ratio-of-means estimator demonstrates remarkable robustness against measurement error in auxiliary variates.
Careful consideration of measurement error is essential when applying ratio estimation techniques.
The choice of ratio estimator can significantly influence the reliability of survey results in the presence of auxiliary variable errors.