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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

8.5K
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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Kendall's Coefficient of Concordance01:20

Kendall's Coefficient of Concordance

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Kendall's Coefficient of Concordance (W), also known as Kendall's W, is a non-parametric statistical measure used to assess the agreement or concordance between multiple raters or judges when they rank a set of items. It is often used when you have ordinal data (ranks) and you want to see if there is consistency or consensus among the raters. It is widely applied in research areas such as psychology, medicine, and social sciences, where multiple judges are asked to rank or rate subjects...
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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...
8.4K
Confidence Intervals01:21

Confidence Intervals

9.2K
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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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...
9.8K
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

8.5K
A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
8.5K

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Related Experiment Video

Updated: Nov 17, 2025

Isokinetic Robotic Device to Improve Test-Retest and Inter-Rater Reliability for Stretch Reflex Measurements in Stroke Patients with Spasticity
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Generalized confidence interval for an agreement between raters.

Dulal K Bhaumik1,2, Hairong Shi2, Domenic J Reda2

  • 1Department of Psychiatry, University of Illinois at Chicago, Chicago, Illinois, USA.

Statistics in Medicine
|February 12, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a generalized confidence interval (GCI) for the concordance correlation coefficient (CCC) to improve statistical agreement assessment in small samples. The new method offers reliable inference for inter-rater reliability when traditional tests fail.

Keywords:
agreementconcordance correlation coefficientcoverage probabilitygeneralized confidence interval

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Area of Science:

  • Statistics
  • Biostatistics
  • Medical Informatics

Background:

  • Statistical assessment of agreement among raters is crucial but lacks robust inferential methods, especially for small sample sizes.
  • The complex nature of the concordance correlation coefficient (CCC) hinders the development of reliable statistical tests for inter-rater agreement.
  • Existing large sample-based methods for CCC often perform poorly with limited data, necessitating new approaches for small sample inference.

Purpose of the Study:

  • To develop and evaluate inferential procedures for assessing statistical agreement among raters using the concordance correlation coefficient (CCC), particularly for small sample sizes.
  • To construct a generalized confidence interval (GCI) for CCC that performs reliably even with limited data.
  • To compare the performance of the proposed GCI with a large sample-based confidence interval (LSCI).

Main Methods:

  • Construction of a generalized confidence interval (GCI) for the concordance correlation coefficient (CCC) based on a bivariate normal distribution.
  • Development of a large sample-based confidence interval (LSCI) for comparative analysis.
  • Simulation studies were conducted to assess the coverage probability (CP) and performance of the GCI.

Main Results:

  • The generalized confidence interval (GCI) demonstrated satisfactory performance, achieving desired coverage probabilities in simulation studies.
  • The GCI provides a more reliable method for statistical inference of agreement compared to traditional methods in small samples.
  • Comparison with the large sample-based confidence interval (LSCI) highlighted the advantages of the GCI for small sample data.

Conclusions:

  • The developed generalized confidence interval (GCI) offers a valuable tool for accurate statistical assessment of agreement among raters, especially when dealing with small sample sizes.
  • The study addresses a critical gap in statistical inference for inter-rater reliability, providing a practical solution for researchers.
  • The findings suggest that hypothesis testing of CCC might have limited practical value without robust confidence intervals, particularly in the absence of a gold standard.