Читать книгу Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis - Страница 20

Statistical thinking is all about relativity. Statistics are not about numbers, they are about distributions of numbers (Green, 2000, personal communication). Rarely in statistics, or science for that matter, do we evaluate things in a vacuum.

Consider a very easy example. You board an airplane destined to your favorite vacation spot. How talented is the pilot who is flying your airplane? Is he a “good” pilot or a “bad” pilot? One would hope he is “good enough” to fulfill his duties and ensure your and other passengers' safety. However, when you start thinking like a statistician, you may ponder the thought of how good of a pilot he is relative to other pilots. Where on the curve does your pilot fall? In terms of his or her skill, the pilot of an airplane can be absolutely good, but still relatively poor. Perhaps that pilot falls on the lower end of the talent curve for pilots. The pilot is still very capable of flying the plane, they have passed an absolute standard, but he or she just isn't quite as good as most other pilots (see Figure 1.5).

We can come up with a lot of other examples to illustrate the absolute versus relative distinction. If someone asked you whether you are intelligent, ego aside, as a statistician, you may respond “relative to who?” Indeed, with a construct like IQ, relativity is all we really have. What does absolute intelligence look like? Should our species discover aliens on another planet one day, we may need to revise our definition of intelligence if such are much more (or much less) advanced than we are. Though of course, this would assume we have the intelligence to comprehend that their capacities are more than ours, a fact not guaranteed and hence another example of the trap of relativity.

Relativity is a benchmark used to evaluate much phenomena, from intelligence to scholastic achievement to prevalence of depression, and indeed much of human and nonhuman behavior. Understanding that events witnessed could be theorized to have come from known distributions (like the talent distribution of pilots) is a first step to thinking statistically. Most phenomena have distributions, either known or unknown. Statistics, in large part, is a study of such distributions.

Figure 1.5 The “pilot criterion” must be met for any pilot to be permitted to fly your plane. However, of those skilled enough to fly, your pilot may still lay at the lower end of the curve. That is, your pilot may be absolutely good, but relatively poor in terms of skill.