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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

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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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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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.
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Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

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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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An R-Based Landscape Validation of a Competing Risk Model
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Confidence interval construction for proportion difference from partially validated series with two fallible

Shi-Fang Qiu1, Li-Ming Wang1,2, Man-Lai Tang3

  • 1Department of Statistics and Data Science, Chongqing University of Technology, Chongqing, China.

Journal of Biopharmaceutical Statistics
|May 10, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for constructing confidence intervals (CI) for the difference between two proportions when classifiers are fallible. Recommended methods offer reliable estimation for proportion difference analysis.

Keywords:
Bayesian methodBootstrap resamplingconfidence intervalfallible classifiermethod of variance estimates recovery

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Inference

Background:

  • Accurate estimation of proportion differences is crucial in various scientific fields.
  • Partially validated classifiers and double-sampling schemes present unique statistical challenges.
  • Existing methods may not adequately address the fallibility of classifiers in proportion difference estimation.

Purpose of the Study:

  • To develop and evaluate confidence interval (CI) construction methods for the difference between two independent proportions.
  • To address scenarios involving partially validated classifiers and a double-sampling scheme.
  • To compare the performance of various CI methods under different statistical models.

Main Methods:

  • Development of several confidence intervals (CIs) using variance estimates recovery.
  • Application of asymptotic, bootstrap, and Bayesian methods for combining confidence limits.
  • Evaluation of methods under two models: independence and dependence.
  • Utilizing simulation studies to assess CI performance.

Main Results:

  • Most developed CIs performed well under the independence model, with exceptions noted for bootstrap percentile-t and Bayesian credible intervals (with uniform prior).
  • All tested CIs performed well under the dependence model.
  • The study recommends specific CI methods based on simulation outcomes.

Conclusions:

  • The proposed methods provide reliable confidence intervals for proportion differences in complex scenarios.
  • The choice of CI method is influenced by the underlying statistical model (independence vs. dependence).
  • The findings offer practical guidance for researchers using fallible classifiers in double-sampling studies.