Power Law Phenomena and Statistics

Bill McKelvey, Anderson Management School, University of California at Los Angeles

In power law functions the exponent stays constant whereas in normal exponentials the exponential varies. On occasion, deviation amplifying mutual causal processes among interdependent data points cause extreme events characterized by a power law. Power laws seem ubiquitous; we list 68 of them—half each among natural and social phenomena. We draw a “line in the sand” between Gaussian (based on independent data points, finite variance and emphasizing averages) and Paretian statistics (based on interdependence, positive feedback, infinite variance, and emphasizing extremes). Quantitative journal publication depends almost entirely on Gaussian statistics. There is a disjunction. Managers live mostly in a world of extremes. We draw on complexity and earthquake sciences to propose redirecting organization science. Conclusion: No statistical findings should be accepted into organization science if they gain significance via some assumption-device by which extreme events and infinite variance are ignored.

Keywords: Power laws; Gaussian; Pareto; Mandelbrot; distribution, robustness, interdependence; positive feedback; extremes; complexity; earthquakes; normal science