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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 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...
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...
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...
Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...

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Assessment and Communication for People with Disorders of Consciousness
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Covariate-adjusted confidence interval for the intraclass correlation coefficient.

Mohamed M Shoukri1, Allan Donner, Abdelmoneim El-Dali

  • 1National Biotechnology Center, KFSHRC, Saudi Arabia. shoukri@kfshrc.edu.sa

Contemporary Clinical Trials
|July 23, 2013
PubMed
Summary

Accurately estimating sample size for cluster sampling requires understanding the intracluster correlation coefficient (ICC). Covariate design significantly impacts ICC estimation, influencing the overall study design effect.

Keywords:
Generalized Estimating EquationsIntra-class correlationMonte-Carlo simulationsMulti-level modelsPercentile bootstrap confidence intervals

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Sample size estimation is critical for study design, particularly in cluster sampling.
  • The design effect, influenced by average cluster size and intracluster correlation coefficient (ICC), determines sample size.
  • Hierarchical and generalized linear models can reduce residual error by incorporating covariates.

Purpose of the Study:

  • To investigate how covariate design (cluster-level vs. within-cluster) affects ICC estimation and, consequently, the design effect.
  • To emphasize the importance of distinguishing covariate types at the study design stage.
  • To assess the accuracy of ICC estimation and confidence interval coverage for ICC using the nested-bootstrap method and Monte Carlo simulations.

Main Methods:

  • Utilized the nested-bootstrap method to evaluate ICC estimation accuracy for continuous and binary outcomes under varying covariate structures.
  • Employed Monte Carlo simulations to assess estimator efficiency and the accuracy of 95% confidence interval coverage for the population ICC.
  • Provided SAS macro code to aid in constructing confidence intervals for the ICC.

Main Results:

  • Demonstrated that the way covariates are incorporated into the model (cluster-level vs. within-cluster) significantly impacts ICC estimation.
  • Found that the covariate design directly influences the design effect, a key component of sample size calculations.
  • Validated the nested-bootstrap method and Monte Carlo simulations for assessing ICC estimation and confidence interval accuracy.

Conclusions:

  • The choice of covariate design is a crucial factor in accurately estimating the intracluster correlation coefficient and the design effect in cluster sampling studies.
  • Researchers must carefully consider and specify covariate measurement levels during the study design phase to ensure appropriate sample size calculations.
  • The presented methods and tools can enhance the reliability of sample size estimations in complex cluster sampling designs.