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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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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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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.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
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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.
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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An R-Based Landscape Validation of a Competing Risk Model
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Smooth bootstrap-based confidence intervals for one binomial proportion and difference of two proportions.

Dongliang Wang1, Alan D Hutson2

  • 1Department of Public Health and Preventive Medicine, State University of New York Upstate Medical University, 750 East Adams Street, Syracuse, NY 13210, USA.

Journal of Applied Statistics
|March 18, 2016
PubMed
Summary

A new smooth bootstrap method improves confidence intervals for binomial proportions, especially for the difference between two proportions. This approach offers superior coverage probabilities, particularly in critical tail regions, enhancing binary data analysis.

Keywords:
binary databootstrapconfidence intervalproportionquantile function

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Confidence intervals (CIs) are crucial for analyzing binary data.
  • Existing methods for binomial proportions have limitations, especially in two-sample settings.

Purpose of the Study:

  • To introduce a novel bootstrap procedure for constructing confidence intervals for binomial proportions.
  • To enhance the accuracy of confidence intervals, particularly for the difference between two proportions.

Main Methods:

  • A new bootstrap procedure using a smooth quantile function for discrete data.
  • Resampling techniques applied to estimate confidence intervals.
  • Comparative simulation studies to evaluate performance.

Main Results:

  • The proposed method demonstrates superior or comparable coverage probabilities in the one-sample setting.
  • The smooth bootstrap CIs show significantly improved, near-uniform coverage for the difference between two proportions, outperforming existing methods in tail regions.

Conclusions:

  • The novel smooth bootstrap approach offers a robust and accurate method for confidence interval estimation.
  • This technique is particularly advantageous for analyzing the difference between two binomial proportions in binary data sets.