Beyond Gaussian averages: redirecting international business and management research toward extreme events and power law
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Beyond Gaussian averages: redirecting international business and management research toward extreme events and power laws Pierpaolo Andriani1 and Bill McKelvey2 1
Durham Business School, Durham, UK; The UCLA Anderson School of Management, Los Angeles, CA, USA 2
Correspondence: Bill McKelvey, The UCLA Anderson School of Management, 110 Westwood Plaza, Los Angeles, CA 90095-1481, USA. Tel: þ 1 310 825 7796; Fax: þ 1 310 206-2002; E-mail: [email protected]
Abstract Practicing managers live in a world of ‘extremes’, but international business and management research is based on Gaussian statistics that rule out such extremes. On occasion, positive feedback processes among interactive data points cause extreme events characterized by power laws. They seem ubiquitous; we list 80 kinds of them – half each among natural and social phenomena. We use imposed tension and Per Bak’s ‘self-organized criticality’ to argue that Pareto-based science and statistics (based on interdependence, positive feedback, scalability, (nearly) infinite variance, and emphasizing extremes) should parallel the traditional dominance of Gaussian statistics (based on independent data points, finite variance and emphasizing averages). We question quantitative journal publications depending on Gaussian statistics. The cost is inaccurate science and irrelevance to practitioners. In conclusion, no statistical findings should be accepted into business studies if they gain significance via some assumption device by which extreme events and (nearly) infinite variance are ignored. Accordingly, we suggest redirecting international business studies, and management research in general. Journal of International Business Studies (2007) 38, 1212–1230. doi:10.1057/palgrave.jibs.8400324 Keywords: power laws; fractals; Gaussian; Pareto; interdependence; extremes
Introduction The most diverse attempts continue to be made to discredit in advance all evidence based on the use of doubly logarithmic graphs. But we think this method would have remained uncontroversial, were it not for the nature of the conclusion to which it leads. Unfortunately, a straight, doubly logarithmic graph indicates a distribution that flies in the face of the Gaussian dogma, which long ruled uncontested. The failure of applied statisticians and social scientists to heed Zipf helps account for the striking backwardness of their fields (Mandelbrot, 1983: 404).
Received: 19 July 2006 Revised: 4 April 2007 Accepted: 2 August 2007 Online publication date: 18 October 2007
Most quantitative business studies researchers presume Gaussian (normal) distributions with finite means and variances and use appropriate statistics to match: for evidence, study any random sample of current research papers of your choosing. It follows that virtually all of our quantitative research-based lessons to managers stem from Gaussian-based research. On the other hand, best-selling
Beyond Gaussian averages
Pierpaolo A
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