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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

11.5K
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 confidence...
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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

Confidence Interval for Estimating Population Mean

9.5K
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...
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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...
12.7K
Confidence Coefficient01:24

Confidence Coefficient

11.1K
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...
11.1K
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

10.0K
To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
10.0K

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An R-Based Landscape Validation of a Competing Risk Model
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Confidence interval construction for the difference between two correlated proportions with missing observations.

Nian-Sheng Tang1, Hui-Qiong Li1, Man-Lai Tang2

  • 1a Department of Statistics , Yunnan University , Kunming , P. R. China.

Journal of Biopharmaceutical Statistics
|January 31, 2015
PubMed
Summary

This study introduces eight confidence intervals (CIs) for correlated proportions with missing data. Wilson score and Wald-type CIs with constrained maximum likelihood estimates are recommended for accurate and narrow interval estimation.

Keywords:
Bootstrap confidence intervalcorrelated proportion differencemissing datapaired binary datasquaring-and-adding confidence interval

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Area of Science:

  • Biostatistics
  • Statistical Inference
  • Data Analysis

Background:

  • Incomplete paired binary data present challenges in statistical analysis.
  • Accurate confidence intervals (CIs) are crucial for estimating the difference between two correlated proportions.

Purpose of the Study:

  • To construct and evaluate eight confidence intervals for the difference between two correlated proportions with missing paired binary data.
  • To identify the most reliable CIs for small-to-moderate sample sizes.

Main Methods:

  • Construction of eight CIs using likelihood ratio, score, Wald-type, hybrid (Wilson score, Agresti-Coull), and Bootstrap methods.
  • Simulation studies to assess CI performance based on coverage probability and interval width.
  • Application to a neurological study dataset.

Main Results:

  • The Wilson-score-based hybrid CI and Wald-type CI with constrained maximum likelihood estimates demonstrated superior performance.
  • These CIs exhibited empirical coverage probabilities close to the nominal level.
  • They also provided shorter expected interval widths and balanced non-coverage probabilities.

Conclusions:

  • The Wilson-score-based hybrid CI and Wald-type CI are recommended for analyzing correlated proportions with missing data.
  • These methods offer improved accuracy and precision, particularly in small-to-moderate sample sizes.
  • The findings are applicable to various fields, including neurological research.