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Related Concept Videos

Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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...
Confidence Intervals01:21

Confidence Intervals

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...
Confidence Coefficient01:24

Confidence Coefficient

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 both the...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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 't,' or...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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...
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

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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An R-Based Landscape Validation of a Competing Risk Model
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An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Recommended confidence intervals for two independent binomial proportions.

Morten W Fagerland1, Stian Lydersen2, Petter Laake3

  • 1Unit of Biostatistics and Epidemiology, Oslo University Hospital, Norway. morten.fagerland@medisin.uio.no.

Statistical Methods in Medical Research
|October 15, 2011
PubMed
Summary

Comparing confidence intervals for two independent binomial proportions is crucial. This study evaluates various methods, recommending optimal choices for different sample sizes to ensure accurate estimation of treatment effects.

Keywords:
2 × 2 tableNNTodds ratiorelative riskrisk difference

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Establishing a Competing Risk Regression Nomogram Model for Survival Data
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An R-Based Landscape Validation of a Competing Risk Model
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Published on: September 16, 2022

Establishing a Competing Risk Regression Nomogram Model for Survival Data
04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

  • Biostatistics
  • Statistical Inference
  • Clinical Trials

Background:

  • Estimating the relationship between two independent binomial proportions is common in research.
  • Common metrics include difference, number needed to treat, ratio, and odds ratio.
  • Existing confidence intervals can yield significantly different results, impacting interpretation.

Purpose of the Study:

  • To describe and compare approximate and exact confidence intervals for binomial proportions.
  • To evaluate the performance of various confidence intervals across different sample sizes.
  • To provide recommendations for selecting appropriate confidence intervals.

Main Methods:

  • Review and comparison of traditional (e.g., Wald, Katz) and modern confidence intervals.
  • Assessment of interval performance, particularly concerning accuracy and ease of calculation.
  • Illustrative examples using small and moderate-to-large sample sizes.

Main Results:

  • Traditional intervals like Wald and Katz perform poorly with small sample sizes.
  • Several approximate and exact intervals demonstrate better performance and are readily available.
  • Interval selection significantly impacts the estimation of treatment effects.

Conclusions:

  • Careful selection of confidence intervals is essential for reliable estimation of binomial proportion relationships.
  • Recommendations are provided for optimal interval choice based on sample size.
  • Accessible and accurate confidence intervals are available for practical application.