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A Comparison of Methods for Constructing Confidence Intervals for the Squared Multiple Correlation Coefficient.

J Algina

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    This study compared four methods for calculating confidence intervals for the population squared multiple correlation coefficient (r²). The method using the R² distribution is recommended for its accurate coverage probability under multivariate normality.

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    Area of Science:

    • Statistics
    • Psychometrics
    • Quantitative Psychology

    Background:

    • Accurate confidence intervals are crucial for estimating the population squared multiple correlation coefficient (r²).
    • Existing approximate methods may exhibit poor performance in certain scenarios.
    • The squared multiple correlation coefficient (r²) is a key measure of effect size in regression analyses.

    Purpose of the Study:

    • To compare the performance of four distinct methods for constructing confidence intervals for the population squared multiple correlation coefficient (r²).
    • To identify the most reliable method for estimating the precision of r² estimates.

    Main Methods:

    • Comparison of four confidence interval construction methods for the population squared multiple correlation coefficient (r²).
    • One method utilizes the distribution of R².
    • Three methods are based on approximate results from Olkin and Finn (1995).

    Main Results:

    • The confidence interval method based on the distribution of R² demonstrated exact coverage probability (1 - a) under multivariate normality for r² > 0.
    • The three approximate methods showed poor performance across various combinations of r².
    • The exact method provided reliable interval estimation, unlike the approximate approaches.

    Conclusions:

    • The confidence interval method derived from the R² distribution is recommended for its accuracy and reliability.
    • Approximate methods for constructing confidence intervals for r² should be used with caution due to potential performance issues.
    • Researchers should prioritize methods ensuring accurate coverage probability for robust statistical inference.