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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.
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Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction.

Johnson Ching-Hong Li¹, Wai Chan, Ying Cui

¹University of Alberta, Canada The Chinese University of Hong Kong, Shatin, Hong Kong, The People's Republic of China. johnson.li@ualberta.ca

The British Journal of Mathematical and Statistical Psychology

|October 7, 2011

Summary

This study introduces a bootstrap procedure to accurately estimate standard errors and confidence intervals for correlations corrected for indirect range restriction. This method addresses limitations in existing correction algorithms, offering a reliable alternative for statistical analysis.

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Area of Science:

Statistics
Psychometrics
Quantitative Psychology

Background:

Standard Pearson correlation coefficient (r) is biased under indirect range restriction.
Existing correction methods (Thorndike's Case III, Schmidt et al.'s Case IV) lack standard error and confidence interval estimation.
Indirect range restriction occurs when a third variable (Z) restricts both predictor (X) and criterion (Y).

Purpose of the Study:

To propose and evaluate a bootstrap procedure for estimating standard error and confidence intervals.
To correct for bias in correlation coefficients due to indirect range restriction.
To provide a viable alternative to existing correction algorithms for statistical inference.

Main Methods:

Developed a bootstrap procedure for estimating standard error and confidence intervals.
Conducted two Monte Carlo simulations to assess the bootstrap procedure's performance.
Evaluated accuracy across various simulation conditions, including selection ratio and sample size.

Main Results:

The bootstrap procedure demonstrated generally accurate estimation of standard error and confidence intervals.
Performance remained consistent across different simulation conditions.
The proposed method proved effective in addressing the limitations of prior correction algorithms.

Conclusions:

The bootstrap procedure offers a reliable method for estimating standard error and confidence intervals for correlations corrected for indirect range restriction.
This approach enhances statistical inference in situations with indirect range restriction.
The bootstrap method serves as a valuable alternative for researchers in quantitative fields.