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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.
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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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 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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Sample Proportion and Population Proportion01:20

Sample Proportion and Population Proportion

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Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...
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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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Ensemble confidence intervals for binomial proportions.

Hayeon Park1, Lawrence M Leemis1

  • 1Department of Mathematics, The College of William & Mary, Williamsburg, Virginia.

Statistics in Medicine
|May 18, 2019
PubMed
Summary

We introduce new ways to measure confidence interval performance for binomial proportions. An Ensemble confidence interval improves statistical properties by combining existing methods, with R software available for use.

Keywords:
binomial distributionconfidence intervalcoveragestatistical computing

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Area of Science:

  • Statistics
  • Statistical inference
  • Computational statistics

Background:

  • Confidence intervals are crucial for estimating binomial proportions.
  • Existing approximate confidence intervals have limitations in performance.
  • Accurate performance metrics are needed for interval evaluation.

Purpose of the Study:

  • To propose and evaluate performance measures for confidence intervals of binomial proportions.
  • To develop a novel 'Ensemble' confidence interval with enhanced statistical properties.
  • To provide accessible software for implementing and assessing these methods.

Main Methods:

  • Defined root mean squared error and mean absolute deviation as performance metrics.
  • Developed an 'Ensemble' confidence interval by combining existing approximate intervals based on coverage functions.
  • Utilized R programming language for software development and distribution via CRAN.

Main Results:

  • The proposed Ensemble confidence interval demonstrates improved statistical properties compared to individual constituent intervals.
  • The developed performance measures allow for a robust assessment of confidence interval accuracy.
  • An R package is available, facilitating the practical application of these statistical tools.

Conclusions:

  • The Ensemble confidence interval offers a superior approach for estimating binomial proportions.
  • The new performance metrics provide a valuable framework for evaluating statistical intervals.
  • The readily available R software promotes wider adoption and application in statistical practice.