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Related Concept Videos

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.
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Interpretation of Confidence Intervals01:19

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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 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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Uncertainty: Confidence Intervals00:54

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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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Confidence Interval for Estimating Population Mean01:25

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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...
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Testing a Claim about Population Proportion01:24

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A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
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Calibrated Bayesian Credible Intervals for Binomial Proportions.

Robert H Lyles1, Paul Weiss1, Lance A Waller1

  • 1Department of Biostatistics and Bioinformatics, The Rollins School of Public Health of Emory University, 1518 Clifton Rd. N.E., Mailstop 1518-002-3AA, Atlanta, GA 30322.

Journal of Statistical Computation and Simulation
|October 5, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a novel confidence interval for binomial proportions, balancing width and coverage. It offers improved performance over traditional methods by optimizing Bayesian credible intervals using tailored Beta priors.

Keywords:
Approximate inferenceConfidence intervalExact inferenceLower boundUpper bound

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Area of Science:

  • Statistics
  • Biostatistics
  • Computational Statistics

Background:

  • Traditional confidence intervals for binomial proportions, such as Wald and Clopper-Pearson, have recognized limitations.
  • Existing alternatives include score test-based intervals, exact testing adaptations, and Bayesian credible intervals using various priors.

Purpose of the Study:

  • To propose and evaluate a new confidence interval for binomial proportions that offers an optimal balance between interval width and coverage properties.
  • To develop a method that provides an intermediate solution between the Clopper-Pearson and Jeffreys intervals.

Main Methods:

  • A novel interval strategy is proposed, selecting a parameter κ (0 to 0.5) based on coverage criteria.
  • Lower and upper limits of the credible interval are derived from Beta(κ, 1-κ) and Beta(1-κ, κ) priors, respectively.
  • The method optimizes interval width computationally while ensuring average lower and upper coverage rates are less than or equal to α/2 across specified regions.

Main Results:

  • The proposed interval demonstrates improved coverage balance compared to existing methods.
  • The interval's behavior can be tuned towards Jeffreys or Clopper-Pearson intervals by adjusting coverage criteria and region widths.
  • Computational optimization readily achieves interval width targets subject to coverage constraints.

Conclusions:

  • The recommended new confidence interval offers a valuable alternative for estimating binomial proportions, providing superior coverage balance.
  • This approach addresses the drawbacks of traditional intervals by offering a flexible and computationally efficient Bayesian-derived solution.