Note on a Confidence Interval for the Squared Semipartial Correlation Coefficient

Abstract

A squared semipartial correlation coefficient (ΔR²) is the increase in the squared multiple correlation coefficient that occurs when a predictor is added to a multiple regression model. Prior research has shown that coverage probability for a confidence interval constructed by using a modified percentile bootstrap method with ΔR² was generally good with sample sizes that should not be too challenging for educational and psychological researchers. However, that research was limited to values of Δρ² = .00 or Δρ² ≥ .05. The present research investigates coverage probability when .01 ≤ Δρ² ≤ .04 and shows that the modified percentile bootstrap typically results in coverage probability in the [.925, .975] interval for a 95% confidence interval, provided the sample size is at least 50 if the number of predictors in the model with more predictors (i.e., the full model) is four or smaller, at least 150 if the number of predictors in the full model is five or six, and at least 200 and preferably 250 if the number of predictors in the full model is between seven and nine.