New research challenges statistical assumptions

Data drives decision-making in numerous areas, from climate models to public health predictions. But according to Richard Vogel, Professor Emeritus in the Department of Civil and Environmental Engineering at Tufts University, some of those decisions are based on shaky ground. In two recent papers, Vogel uncovers how extremely heavy-tailed data can quietly distort results across most disciplines. His work calls for a more careful, informed use of statistics in an age when data drives nearly every major decision. Importantly, he advocates much greater educational emphasis on the theory of probability, which is the foundation of all statistical methods.

One paper, “When Heavy Tails Disrupt Statistical Inference,” published in The American Statistician, shows that in many real-world situations, basic statistical methods that researchers rely on every day can give grossly misleading results. Remarkably, many laws and theorems literally break down and become useless when applied to datasets which exhibit extremely heavy tails. Heavy tailed datasets tend to exhibit more outliers than one normally expects and such datasets are increasingly common in the new digital age of data.

Vogel draws on decades of experience in hydrology, where understanding rare events like floods and droughts is crucial. His findings extend beyond water systems, touching on earthquakes, rainfall, landslides, and even bird and plant extinctions. These “heavy tails,” or extreme outliers in data, appear across both natural and social systems and are becoming more common.

“For example, Figure 3 in that paper proves that very basic statistical metrics such as variance, skewness and kurtosis that folks use all the time may be completely meaningless, and most folks are not aware of this. That figure summarizes data from many many fields and shows how ordinary commonly used statistical moments can be completely misleading,” Vogel explains.

Data impacted by severely heavy tails could also impact newer technologies. “Artificial intelligence and machine learning are at their root, statistical methods, so those methods will also break down under extremely heavy tails,” Vogel notes. Most statisticians are not well versed in the impacts of extremely heavy tails. Vogel points out that without several upper level graduate courses in the theory of probability, most of the mathematics relating to extremely heavy tails is largely inaccessible to most scientists, engineers and even statisticians. His work raises timely questions about the reliability of today’s data-driven systems in science, business, and policy. In recognition of these contributions, Vogel received the Walter B. Langbein Lecture Award from the American Geophysical Union in 2023, where he presented his findings to an audience of over 1,000 attendees.

In another recent paper, “The Geometric Mean?” published in Communications in Statistics: Theory and Methods, Vogel examines one of the most commonly used yet misunderstood statistics: the geometric mean. The geometric mean is used in a myriad of disciplines to find an average by multiplying values together instead of adding them like in the arithmetic mean. Many fields including environmental science, economics, and engineering employ the geometric mean to describe proportional growth. Though this measure is widely used, Vogel’s research reveals that it’s often applied without a full understanding of its meaning, limitations and applicability.

The study challenges long-held assumptions about when and how the geometric mean should be used. Vogel shows that while it can be helpful for averaging ratios or efficiencies, its accuracy depends heavily on the type of data being analyzed. Importantly, he shows that in most previous applications of the geometric mean, users of that statistic had little awareness of its properties, interpretation and properties.

He also highlights that in some cases—such as when data follows a lognormal pattern—the geometric mean is identical to the median, which is easier to interpret, understand and even to estimate because it is simply the value that is exceeded 50% of the time. By clarifying when   the geometric mean is useful and when it isn't, Vogel provides researchers and industry professionals with practical guidance for using the geometric mean responsibly and effectively.

Vogel earned his Ph.D. in water resource systems from Cornell University in 1984, the same year he began teaching at Tufts, and has built a distinguished career advancing statistical and systems approaches in hydrology, natural hazards, environmental statistics and water resources engineering. His research spans reservoir operations, water quality, watershed modeling, environmental statistics and the analysis of natural hazards with particular emphasis on floods and droughts. Vogel was elected as a 2017 Fellow of the American Geophysical Union and as a 2020 Distinguished Member of the American Society of Civil Engineers, the highest distinction in both AGU and ASCE. He recently delivered several prestigious lectures including the Walter B. Langbein Lecture at the 2023 American Geophysical Union’s annual meeting and the 2020 Ven Te Chow Award lecture to the American Society of Civil Engineers. In 2025 he gave several invited lectures in Nanjing and Dalian, China. After 33 years of teaching at Tufts, he became Professor Emeritus in 2016 in the Department of Civil and Environmental Engineering.

Learn more about Professor Emeritus Richard Vogel.