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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

2.2K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Confidence Intervals01:21

Confidence Intervals

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Interval Level of Measurement00:55

Interval Level of Measurement

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For effective statistical analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...
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Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Expedited Radiation Biodosimetry by Automated Dicentric Chromosome Identification ADCI and Dose Estimation
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Coverage Intervals.

Sara Stoudt1, Adam Pintar2, Antonio Possolo1

  • 1Smith College, Northampton, MA 01063, USA.

Journal of Research of the National Institute of Standards and Technology
|July 17, 2024
PubMed
Summary
This summary is machine-generated.

This study clarifies coverage intervals for measurement uncertainty, comparing them to statistical intervals. It addresses misunderstandings about Monte Carlo method results for realistic expectations and practical use.

Keywords:
Bayesian modelHodges-LehmannMonte Carlo methodType A evaluationWeibull distributioncoverage intervalmediannon-parametricprediction intervalpredictive intervalreference materialtolerance interval

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Area of Science:

  • Metrology and Measurement Science
  • Applied Statistics
  • Scientific Uncertainty Quantification

Background:

  • Coverage intervals are standard for expressing measurement uncertainty.
  • Existing literature often misinterprets intervals derived from the Monte Carlo method (GUM-S1).

Purpose of the Study:

  • To review and compare GUM coverage intervals with common statistical intervals.
  • To address and clarify common misunderstandings regarding GUM-S1 Monte Carlo intervals.
  • To propose a novel interpretation of GUM-S1 intervals for practical application.

Main Methods:

  • Review of the Guide to the Expression of Uncertainty in Measurement (GUM) definitions.
  • Comparative analysis of coverage intervals against confidence, credible, and tolerance intervals.
  • Focus on interpretation of intervals from Monte Carlo simulations (GUM-S1).

Main Results:

  • Coverage intervals, while formally similar to confidence intervals, are interpreted differently in GUM.
  • Common interpretations of GUM-S1 Monte Carlo intervals can lead to unrealistic expectations.
  • A novel interpretation is proposed to enhance understanding and utility of GUM-S1 intervals.

Conclusions:

  • Clarifying the interpretation of coverage intervals, especially those from GUM-S1, is crucial for accurate uncertainty assessment.
  • The proposed interpretation aims to foster realistic expectations and guide practical application of these intervals.
  • Better understanding of GUM-S1 intervals enhances their usefulness in measurement science.