A Bootstrap Confidence Interval Based on a Correlation Corrected for Range Restriction

The sample correlation coefficient corrected for range restriction was bootstrapped to obtain a confidence interval on the unrestricted population correlation, rho. The technique was evaluated using a computer simulation under different values of rho and four distributions (normal, mixed, positively skewed and negatively skewed). The corrected correlation coefficient yielded accurate bootstrap intervals over the four distributions. On the average, the size of rho did not affect the accuracy of the confidence interval. However, it did affect stability. The interval behaved rather erratically when rho was small (.1) and sample size was small. Sample size was found to be the most important factor in determining accuracy and stability. Overall, the results suggest that bootstrapping the corrected correlation coefficient is a reliable method for obtaining a confidence interval on rho especially when the sample size is moderate to large (n > 50).