Statistics predicts truth? I thought the entire value of statistics was to gain tractability WRT problems where the complete "truth" of the situation is unknown. IOW, we wouldn't need statistics at all if we knew what the truth was.
How can a phenomenon be "random" when by definition it is already "there?" What you seem to suggest is that a concrete something — a phenomenon — is the product of something we don't understand, which is a confession of ignorance.
Rather than settle for ignorance, maybe we should exercise our curiosity about the nature of the world and maybe learn something new.
RE: the Central Limit Theorem I read the following at "The Central Limit Theorem — How to Tame Wild Populations" —
People come in a variety of shapes and sizes. Get a few million people together in one place, say in Rhode Island or South Carolina, and it would be impossible to predict what a single person selected from either state would be like. Try to compare all Rhode Islanders to all South Carolinians and the task gets even more complex. Obviously, something is needed to simplify the process, and that’s why we have statistics.Which, in my fevered imagination, means we have to sacrifice the pursuit of "deep truths" about the natural world in order to make a problem tractable.... In fact, it seems to me science isn't as interested in "deep truths" as it is in solving immediate technical problems.
The article continues:
...we must simplify and so we’ll focus on a parameter that can characterize the weights of all individuals in a population. A parameter is a number which summarizes a specific characteristic generated from measurements of every member of a population. Using a parameter it’s possible to represent a property of an entire population with a single number instead of millions of individual data points.But such an approach wipes out the idea of the value of any individual case. The group becomes the focus. Plus how does one measure every member of the population? More to the point, what is being measured? The measurer selects what he wants to measure, and measures only that.
Nature creates individuals. The idea of the group is a convenient human construct used to "simplify" a complex problem by blending away inconvenient differences. What does this simplification cost you, assuming you want to know the truth of reality?
BTW, if you find these comments mystifying, please be advised that I'm coming at this problem, not as a scientist, but as a philosopher, in terms of the philosophical disciplines of epistemology (the science of knowledge and knowing) and ontology (the science of being and existence).
Well, FWIW.
Thank you as ever for writing, OldNavyVet!
Estimates and predictions can be made quite well using unbiased test data in conjunction with the Central Limit Theorem.
Nothing, however, can be estimated or predicted with 100% confidence; but 90 to 95 percent confidence levels -- as to truth -- are good things to know in the technical world.
Been there, done that ... Have a great day.