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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.
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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.
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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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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.
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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.
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Some Improvements in Confidence Intervals for Standardized Regression Coefficients.

Paul Dudgeon1

  • 1Melbourne School of Psychological Sciences, The University of Melbourne, Parkville, VIC, 3010, Australia. dudgeon@unimelb.edu.au.

Psychometrika
|March 15, 2017
PubMed
Summary
This summary is machine-generated.

This study found that heteroscedastic-consistent (HC) estimators, specifically HC3 and HC5, provide superior confidence intervals for standardized regression coefficients compared to normal theory and asymptotic distribution-free (ADF) methods under non-normal data conditions.

Keywords:
non-normalityrobust confidence intervalsstandardized regression coefficients

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Area of Science:

  • Statistics
  • Psychometrics
  • Econometrics

Background:

  • Consistent confidence intervals for standardized regression coefficients are crucial for statistical inference.
  • Previous work established methods for normal and non-normal data, but limitations exist.

Purpose of the Study:

  • To evaluate heteroscedastic-consistent (HC) estimators for confidence intervals of standardized regression coefficients under non-normal conditions.
  • To compare the performance of HC estimators against normal theory and asymptotic distribution-free (ADF) methods.

Main Methods:

  • A Monte Carlo simulation was employed to assess various confidence interval estimators.
  • Seven heteroscedastic-consistent (HC) estimators were investigated, alongside normal theory and ADF approaches.

Main Results:

  • HC3 and HC5 estimators demonstrated superior performance over ADF and normal theory methods.
  • The HC5 estimator showed greater robustness than HC3 under specific conditions.

Conclusions:

  • HC3 and HC5 estimators are recommended for constructing confidence intervals for standardized regression coefficients with non-normal data.
  • Future research could explore HC estimators for other effect size measures.