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Educational and Psychological Measurement
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Confidence Intervals for an Effect Size Measure in Multiple Linear Regression

James Algina

University of Florida

H. J. Keselman

University of Manitoba

Randall D. Penfield

University of Miami

The increase in the squared multiple correlation coefficient ({Delta}R 2) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. The coverage probability that an asymptotic and percentile bootstrap confidence interval includes {Delta}{rho}2 was investigated. As expected, coverage probability for the asymptotic confidence interval was often inadequate (outside the interval .925 to .975 for a 95% confidence interval), even when sample size was quite large (i.e., 200). However, adequate coverage probability for the confidence interval based on a bootstrap interval could typically be obtained with a sample size of 200 or less, and moreover, this accuracy was obtained with relatively small sample sizes (100 or less) with six or fewer predictors.

Key Words: squared semipartial correlation • multiple correlation • effect size • bootstrap • confidence interval

Educational and Psychological Measurement, Vol. 67, No. 2, 207-218 (2007)
DOI: 10.1177/0013164406292030
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J. Algina, H. J. Keselman, and R. J. Penfield
Note on a Confidence Interval for the Squared Semipartial Correlation Coefficient
Educational and Psychological Measurement, October 1, 2008; 68(5): 734 - 741.
[Abstract] [PDF]