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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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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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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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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...
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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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Critical Values01:31

Critical Values

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A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
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Bootstrap Confidence Intervals for Multilevel Standardized Effect Size.

Mark H C Lai1

  • 1Department of Psychology, University of Southern California, Los Angeles, CA, USA.

Multivariate Behavioral Research
|April 14, 2020
PubMed
Summary
This summary is machine-generated.

Researchers can use bootstrap methods to calculate confidence intervals (CIs) for effect sizes in multilevel studies. The residual bootstrap with studentized CIs offers the best coverage, improving effect size estimation accuracy.

Keywords:
Effect sizebootstrapcluster-randomized trialmultilevelnonnormal datarobustnessstandardized mean difference

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Area of Science:

  • Statistics
  • Biostatistics
  • Methodology

Background:

  • Applied researchers are encouraged to report effect size measures alongside statistical significance tests.
  • Confidence intervals (CIs) for effect size with clustered/multilevel data are under-discussed.
  • Cluster-randomized trials (CRTs) often involve complex multilevel data structures.

Purpose of the Study:

  • To explore the bootstrap as a viable method for obtaining CIs for multilevel standardized mean difference effect size.
  • To compare the performance of analytic and bootstrap procedures for constructing CIs for multilevel effect size.
  • To provide practical guidance for applied researchers using statistical software.

Main Methods:

  • A simulation study compared 17 analytic and bootstrap procedures for CIs.
  • Procedures were evaluated based on empirical coverage rate and width.
  • Data included both normal and nonnormal distributions.
  • An illustrative example using R and the bootmlm package was provided.

Main Results:

  • The residual bootstrap with studentized CI demonstrated the best overall coverage rates (average 94.75%).
  • The residual bootstrap with basic CI showed superior coverage in smaller sample sizes.
  • Both bootstrap procedures outperformed traditional analytic methods for CIs in multilevel effect size estimation.
  • Bootstrap CIs provided better coverage for both normal and nonnormal data.

Conclusions:

  • Bootstrap methods are accessible and effective for calculating CIs for multilevel effect size.
  • Applied researchers should report CIs to accurately represent the uncertainty in effect size estimates.
  • The residual bootstrap with studentized CI is recommended for general use, while the basic CI is useful for small samples.