Confidence Intervals for Squared Semipartial Correlation Coefficients: The Effect of Nonnormality

Abstract

The increase in the squared multiple correlation coefficient (ΔR²) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size was quite large (i.e., larger than 200). However, they also reported that probability coverage for the confidence intervals based on a bootstrap method was typically quite accurate, and moreover, this accuracy was obtained with relatively small sample sizes with six or fewer predictors. They further speculated that nonnormality would likely affect the accuracy of interval coverage. In the present study, the authors investigated the accuracy of coverage probability for confidence intervals obtained by using asymptotic and percentile bootstrap methodology when either predictors, residuals, or both are nonnormal. Coverage probability for asymptotic confidence intervals is poor, but adequate coverage probability can be obtained with reasonable sample sizes by using percentile bootstrap methodology. As well, the authors found that the width of these intervals was relatively precise (i.e., narrow) for the larger cases of sample size investigated.