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Related Concept Videos

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...
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...
Bonferroni Test01:10

Bonferroni Test

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...
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...
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...
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...

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Confidence intervals for a difference between proportions based on paired data.

Man-Lai Tang1, Man-Ho Ling, Leevan Ling

  • 1Department of Mathematics, Hong Kong Baptist University, Hong Kong, People's Republic of China. mltang@math.hkbu.edu.hk

Statistics in Medicine
|October 14, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces new confidence intervals (CIs) for comparing two related proportions using the MOVER method. These novel CIs, especially those using the Phi coefficient and Tango score, show good performance with limited data.

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Area of Science:

  • Biostatistics
  • Statistical Inference
  • Medical Statistics

Background:

  • Comparing two correlated proportions is crucial in various scientific fields.
  • Existing methods may lack robustness in small sample or sparse data scenarios.

Purpose of the Study:

  • To develop and evaluate explicit asymptotic two-sided confidence intervals (CIs) for the difference between two correlated proportions.
  • To assess the performance of novel MOVER-type CIs, particularly with limited data.

Main Methods:

  • Construction of CIs using the Method of Variance of Estimates Recovery (MOVER).
  • Incorporation of Agresti-Coull, Wilson, and Jeffreys CIs for single proportions within the MOVER framework.
  • Evaluation through simulation studies focusing on small samples and sparse data.

Main Results:

  • MOVER-type CIs incorporating the continuity corrected Phi coefficient and Tango score CI demonstrated satisfactory performance.
  • The proposed methods are effective even with small sample sizes and sparse data structures.
  • The study provides practical illustrations using real-world examples.

Conclusions:

  • The developed MOVER-type confidence intervals offer a reliable approach for analyzing the difference between two correlated proportions.
  • These methods are particularly valuable in situations with limited data, enhancing statistical precision.
  • The study contributes practical tools for biostatistical analysis in medical research.