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

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.