- The late W. Edwards Deming.
The broader context of his observation is that, once you go beyond the mere "enumeration" (counting) of discrete objects (and even that gets fraught), you are estimating.
Good stuff. Although some of the algebra will still lose a lot of people. A number of whom will be cherubically grinding healthcare "Big Data" in pursuit of The Next Big Epiphany.
I know my "Sensitivity vs Specificity" and "Bayes" pretty well. See here as well.
Additionally, count me squarely a "Talebist." And, a "Chebyshev"-ist.
"There is no true value of anything."
That applies to "probabilities" as well. When I hear people state "the probability is..." my reflexive reaction is that "you mean your probability estimate is..." Just as with any other type of statistical calculation, so too do "p-values" form distributions. No serious, competent modern analytics practioner takes undergrad axioms such as "set alpha at 0.05" etc seriously anymore. Such conveniences comprise naive methodological dilettantism. You are interested in outcomes differentials, i.e., "expected values" (the multiplied result of prob(x) times the payoff/payout of x) -- the estimated benefit or cost. Just knowing that two means (including regression trendlines) differ "significantly" is of little practical value. We need to be able, as "accurately" as possible estimate the upshot in terms of differential outcomes (be they scientific, clinical, or business/financial.
Knowing such things to finely-grained, stress-tested valuations -- inclusive of assessing "normality" assumptions -- is how Las Vegas makes its money.
The "normal curve" of undergrad stats angst is a model, the expression of a best-case theoretical bi-directionally asymptotically smooth curvilinear exponential function that exists only in theory.
- Chance is lumpy.
- Overconfidence abhors uncertainty.
- Never flout a convention just once.
- Don't talk Greek if you don't know the English translation.
- If you have nothing to say, don't say anything.
- There is no free hunch.
- You can't see the dust if you don't move the couch.
- Criticism is the mother of methodology.
OH, AND ANOTHER THING
Assessing Absolute vs Relative Risk
Say the ambient prevalence of condition "c" is 1 out of 100, or 1%. We select an appropriate random sample of 2,000 subjects, splitting half via a double-blind RCT experiment into control group CG (no tx) and half into treatment group TG that gets tx "t". We find that the post-treatment prevalence of "c" is 8 of out 1,000 (0.8%), whereas, true to form, there are 10 subjects with condition "c" in the 1,000 person CG (1%).
Well, our tx seems to have reduced the relative risk prevalence by 20%, ja?
Yeah, but the absolute risk reduction estimate from this trial is just one one-hundreth of that, 0.2%
Prevalence matters. Along with these other empirical considerations cited above.
See "Estimating the size of the treatment effect."
More to come...