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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

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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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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Prediction Intervals01:03

Prediction Intervals

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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. 
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Constructing Confidence Intervals for Effect Size Measures of an Indirect Effect.

Sunbok Lee1, Man Kit Lei1, Gene H Brody1

  • 1a Center for Family Research , University of Georgia.

Multivariate Behavioral Research
|December 31, 2015
PubMed
Summary

Five methods for constructing confidence intervals for indirect effect ratio measures were compared. For sample sizes over 500, methods performed similarly, but smaller samples required large effect sizes for precise results.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Confidence intervals (CIs) are crucial for interpreting effect size magnitude and precision.
  • Assessing indirect effects in statistical models often involves ratio measures, posing unique challenges for CI construction.

Purpose of the Study:

  • To compare the performance of five distinct methods for constructing confidence intervals for ratio effect size measures of indirect effects.
  • Evaluate methods based on power, coverage rates, Type I error rates, and CI widths.

Main Methods:

  • Percentile bootstrap method
  • Bias-corrected and accelerated (BCa) bootstrap method
  • Delta method
  • Fieller method
  • Monte Carlo method

Main Results:

  • All five CI methods yielded similar results for sample sizes exceeding 500.
  • For samples smaller than 500, CIs were only sufficiently narrow to inform about population effect sizes when the underlying regression coefficients were large.

Conclusions:

  • Method choice for indirect effect CIs may depend on sample size and effect size magnitude.
  • The nature of ratio quantities and distributional assumptions impact CI performance, particularly in smaller samples.