

The Great Misunderstanding

Both statisticians and engineers recognize the mathematical competence of the other, and this is the cause of The Great Misunderstanding. 
The Great Misunderstanding: 

Statisticians know mathematics, as do engineers, but statisticians have also studied mathematical statistics (inference), probability I&II, experimental design, linear models, ordinary regression, generalized linear models which leads to logistic (and probit) regression (Poisson regression, too), multivariate analysis, Bayesian methods, especially recent computational advances, resampling methods, time series, spatial statistics, ... and considerably more. Statisticians also know that engineers^{1} don't know any of this. Thus both statisticians and engineers recognize the mathematics the other has mastered, and they also know that mathematics, however vital to their discipline, is only a small part of their practice. Since neither the statistician nor the engineer knows what he doesn't know^{2}, he^{3} incorrectly assumes that mathematics is the entirety of the other's skill set. Since each knows considerably more than just mathematics, and since the other clearly does not know what "I" know, the other must be an ignoramus. This is The Great Misunderstanding, and (I believe) is the root of the wellknown^{4} schism between engineers and statisticians. Engineers may find it surprising that there is no such rift between statisticians and the other sciences, such as biology and medicine, pharmacology, psychology, and sociology, for example. I believe this is because, as a rule, these scientists do not posses the mathematical skills to pursue a solution apart from the statistician when the latter displays an ignorance of the specific field.^{5} There is another reason too. The physical world follows the rules of physics which are well known (to those who have studied them) while human behavior is influenced by less well understood and less structured rules. Thus the "softer" sciences are more effected by randomness where statistical models may be more appropriate. 
Notes: 

1) If the shoe fits ... 2) Try to make a list of everything you haven't thought of. 3) In English "he" can refer to anyone whose gender is unknown. This is true of many other languages too of course. 4) TECHNOMETRICS^{*} devoted an entire issue to the sorry state of communication between statisticians and engineers, but, in my view, still missed the point. 5) To be fair it should be noted that today statisticians themselves are becoming increasingly aware of how important an understanding of the underlying science (biology, chemistry, physics, ...) is to solving a problem, rather than just manipulating numbers. This is interesting from a historical perspective since all the great statistical thinkers, Laplace, Pearson, Gosset, Fisher, et al., were practitioners first and theoreticians when their practice demanded it. ^{*}TECHNOMETRICS, August 1990, VOL. 32, NO. 3, "Communications Between Statisticians and Engineers/ Physical Scientists," by A. Bruce Hoadley and J. R. Kettenring [Risk] [Hubris] [Misunderstanding]

Mail to Charles.Annis@StatisticalEngineering.com 