Identifying and Analyzing Extremes: Illustrated by CEOs’ Pay and Performance

This article presents statistical methods for identifying outcomes in a given sample that can be inferred as plausible extreme and whether the extremes on two variables are associated. Applications to CEO pay and performance of 50 top-paid CEOs illustrate these methodologies. Thresholds between extremes and nonextremes are found using high probability intervals under the probability distributions that govern sampling variations of the sample extremes. A Bayesian approach is used to compute odds on the association between the extremes of the two variables. The extreme pay—performance analysis of 50 top-paid CEOs reveals astonishing odds in favor of a company being extreme high only on one of the two versus on both variables. The result is considered decisive evidence for a negative association between extreme on CEO pay and extreme on performance among such top-paid CEOs. By contrast, analysis of the nonextreme CEOs yielded no evidence of any association between CEO pay and performance.