It is the quintessence of science, engineering, and numerous other disciplines to make quantitative observations, record them, and then try to make some sense out of the resulting dataset. Quite often, the latter is an easy task, due either to practiced familiarity with the domain or to the fact that the goals of the exercise are undemanding. However, when working at the frontiers of knowledge, this is not the case. Here, one encounters unknown territory, with maps that are sometimes poorly defined and always incomplete.
The question posed above is nontrivial; the path from observation to understanding is, in general, long and arduous. There are techniques to facilitate the journey but these are seldom taught to those who need them most. My own observations, over the past twenty years, have disclosed that, if a functional relationship is nonlinear, or a probability distribution something other than Gaussian, Exponential, or Uniform, then analysts (those who are not statisticians) are usually unable to cope. As a result, approximations are made and reports delivered containing conclusions that are inaccurate and/or misleading.
With scientific papers, there are always peers who are ready and willing to second-guess any published analysis. Unfortunately, there are as well many less mature disciplines which lack the checks and balances that science has developed over the centuries and which frequently address areas of public concern. These concerns lead, inevitably, to public decisions and warrant the best that mathematics and statistics have to offer, indeed, the best that analysts can provide. Since Nature is seldom linear or Gaussian, such analyses often fail to live up to expectations.
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