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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

9.3K
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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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...
9.2K
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

2.9K
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...
2.9K
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...
8.8K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

9.9K
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...
9.9K
Bonferroni Test01:10

Bonferroni Test

2.6K
The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
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Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index
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Weighted profile likelihood-based confidence interval for the difference between two proportions with paired binomial

Vivek Pradhan1, Krishna K Saha, Tathagata Banerjee

  • 1Pfizer Inc., 200 Cambridge Park Drive, Cambridge, MA 02140, U.S.A.

Statistics in Medicine
|March 7, 2014
PubMed
Summary

New confidence intervals (CIs) for paired binomial proportions offer improved accuracy. Weighted profile likelihood CIs and Jeffreys intervals demonstrate superior coverage probabilities and competitive lengths in statistical comparisons.

Keywords:
bivariate copulaconfidence intervalpaired binomial distributionprofile likelihoodvariance estimate recovery

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Area of Science:

  • Biostatistics
  • Statistical Inference
  • Medical Research

Background:

  • Paired binomial proportions are crucial in biomedical studies.
  • Existing confidence intervals (CIs) for paired binomial proportions have limitations.
  • Methods by Tang et al. and Agresti & Min provide benchmarks.

Purpose of the Study:

  • To propose novel weighted profile likelihood-based confidence intervals (CIs) for the difference between paired binomial proportions.
  • To evaluate the performance of these new CIs against existing methods.
  • To offer improved statistical tools for biomedical data analysis.

Main Methods:

  • Development of weighted profile likelihood for paired binomial data.
  • Adjustment of cell frequencies in 2x2 tables, inspired by Agresti & Min.
  • Numerical simulations to compare CIs based on coverage probability and expected length.

Main Results:

  • Weighted profile likelihood CIs and Jeffreys intervals exhibit superior coverage probabilities.
  • These proposed intervals are competitive in terms of expected lengths.
  • The new methods provide a more reliable inference for paired binomial data.

Conclusions:

  • Weighted profile likelihood-based CIs are recommended for paired binomial proportion inference.
  • These intervals offer enhanced accuracy and efficiency in biomedical applications.
  • The study provides valuable statistical methods for analyzing paired binary outcomes.