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Related Concept Videos

Range Rule of Thumb to Interpret Standard Deviation01:13

Range Rule of Thumb to Interpret Standard Deviation

The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height of...
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
Range00:59

Range

The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount - 16 ounces of liquid, was not...
Accuracy and Precision01:52

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.  Highly accurate measurements...
Accuracy and Precision01:52

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.  Highly accurate measurements...
Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...

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An Automated System for Sound Localization Testing in Hearing-Impaired Listeners
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Published on: March 13, 2026

Inference on the symmetric-range accuracy.

K Krishnamoorthy1, Thomas Mathew

  • 1Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70508, USA. krishna@louisiana.edu

The Annals of Occupational Hygiene
|December 6, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a method to measure sampler accuracy (A), defining it as the range of measurements around a true value. The proposed statistical approach provides reliable accuracy estimates, even with limited data, for applications like air quality monitoring.

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Area of Science:

  • Environmental Science
  • Statistics
  • Analytical Chemistry

Background:

  • Accurate environmental monitoring relies on precise samplers.
  • Quantifying sampler accuracy is crucial for data reliability.
  • Existing methods may lack precision or applicability to small datasets.

Purpose of the Study:

  • To define and provide an explicit expression for symmetric-range accuracy (A) of samplers.
  • To develop confidence limits for this accuracy measure.
  • To offer a convenient approximation for practical application.

Main Methods:

  • Defined symmetric-range accuracy (A) for sampler measurements.
  • Assumed a normal distribution for sampler measurements.
  • Developed confidence limits using a 'generalized confidence interval' concept.
  • Utilized Monte Carlo simulations for evaluation.

Main Results:

  • An explicit expression for symmetric-range accuracy (A) was derived.
  • A novel method for calculating confidence limits for A was proposed.
  • A convenient approximation for confidence limit computation was provided.
  • Monte Carlo evaluation confirmed the method's satisfactory performance, even with small sample sizes.

Conclusions:

  • The proposed statistical methods offer a robust way to assess sampler accuracy.
  • The generalized confidence interval approach provides reliable accuracy estimates.
  • The methods are effective for small sample sizes, enhancing applicability in real-world monitoring scenarios.
  • The approach is demonstrated with carbon monoxide monitoring data.