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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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Computing confidence intervals for standardized regression coefficients.

Jeff A Jones1, Niels G Waller1

  • 1Department of Psychology.

Psychological Methods
|October 2, 2013
PubMed
Summary
This summary is machine-generated.

The standard method for confidence intervals of standardized regression coefficients often fails. The delta method and bootstrap procedures provide accurate coverage rates, especially with large R² values.

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Area of Science:

  • Statistics
  • Psychometrics
  • Regression Analysis

Background:

  • Standard methods for confidence intervals (CIs) of standardized regression coefficients have limitations.
  • These methods may not account for sampling variability in standard deviations, particularly with random predictors.

Purpose of the Study:

  • To evaluate the accuracy of standard and alternative methods for computing CIs of standardized regression coefficients.
  • To identify conditions under which the standard method performs adequately and when it fails.

Main Methods:

  • A Monte Carlo simulation was employed using 36 diverse populations.
  • Empirical confidence interval coverage rates were computed for the standard method and four alternatives: noncentrality interval estimation, delta method, percentile bootstrap, and bias-corrected and accelerated bootstrap.

Main Results:

  • The standard method showed accurate coverage rates under various conditions (sample size, predictor correlations, R²).
  • Coverage rates for the standard method frequently fell below nominal levels when population R² was large and β approached the last eigenvector of RX.
  • The delta method and bootstrap procedures consistently yielded accurate coverage rates in these challenging conditions.

Conclusions:

  • The standard method for CIs of standardized regression coefficients is not universally accurate.
  • The delta method and bootstrap procedures are recommended for evaluating the sampling variability of standardized regression coefficients, particularly in complex models or with large R².
  • Researchers should consider alternative methods to ensure reliable confidence interval estimation.