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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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Interpretation of Confidence Intervals01:19

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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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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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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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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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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Accurate Confidence and Bayesian Interval Estimation for Non-centrality Parameters and Effect Size Indices.

Kaidi Kang1, Megan T Jones2, Kristan Armstrong3

  • 1Department of Biostatistics, Vanderbilt University, 2525 West End Ave.,#1136, Nashville, TN, 37203, USA. kaidi.kang@vanderbilt.edu.

Psychometrika
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PubMed
Summary

Reporting effect size index estimates with confidence intervals (CIs) is crucial. A robust effect size index (RESI) and specific intervals offer valid inference, even with violated assumptions, improving statistical reporting.

Keywords:
analysis of effect sizebayesian bootstrapbootstrapconfidence intervalcredible intervaleffect sizenon-central Chi-squared distributionnon-central F distributionnon-centrality parameterrobust effect size index

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Area of Science:

  • Statistics
  • Quantitative Psychology
  • Biostatistics

Background:

  • Effect size reporting enhances evidence communication.
  • Existing indices have limitations in applicability.
  • A robust effect size index (RESI) was previously proposed for broader data types.

Purpose of the Study:

  • To develop and evaluate RESI estimators and confidence/credible intervals.
  • To assess the performance of different covariance estimators for RESI.
  • To establish a unified procedure for effect size reporting.

Main Methods:

  • Utilized statistical theory and simulations.
  • Developed and evaluated RESI estimators.
  • Investigated confidence intervals (CIs) and credible intervals using various covariance estimators.

Main Results:

  • Covariate randomness negatively impacts Chi-squared and F CIs coverage.
  • Standard CIs for RESI estimators showed inadequate coverage.
  • Nonparametric bootstrap and Bayesian intervals with the robust RESI estimator provided valid inference.

Conclusions:

  • Robust RESI estimator with bootstrap or Bayesian intervals ensures valid statistical inference.
  • This approach is effective even when model assumptions are not fully met.
  • A unified effect size reporting procedure, compatible with ANOVA tables, is proposed.