Using a Nonparametric Bootstrap to Obtain a Confidence Interval for Pearson's r with Cluster Randomized Data: A Case Study

A nonparametric bootstrap was used to obtain an interval estimate of Pearson's r, and test the null hypothesis that there was no association between 5th grade students' positive substance use expectancies and their intentions to not use substances. The students were participating in a substance use prevention program in which the unit of randomization was a public middle school. The bootstrap estimate indicated that expectancies explained 21% of the variability in students' intentions (r = 0.46, 95% CI = [0.40, 0.50]). This case study illustrates the use of a nonparametric bootstrap with cluster randomized data and the danger posed if outliers are not identified and addressed. Editors' Strategic Implications: Prevention researchers will benefit from the authors' detailed description of this nonparametric bootstrap approach for cluster randomized data and their thoughtful discussion of the potential impact of cluster sizes and outliers.