Some sources claim that IQ is correlated with academic and/or professional success. Let's assume there is a correlation of 0.5 between IQ and University GPA, discovered from a study of a very large group of students.

If I took an IQ test and got a score of 100, does this mean I'm less likely to achieve a high GPA? I recently heard a phrase "statistics mean nothing to the individual", meaning (I think) that just because you contracted some illness with a 95% mortality rate, that there's a 5% chance that you'll survive -- that it is incorrect to make some conclusion about an individual based off of the bigger picture derived from a large sample size.

I've read about the Ecological Fallacy (https://en.wikipedia.org/wiki/Ecological_fallacy), but that seems to apply more to summarized metrics like the mean -- you can't assume any given data-point will be close to the mean, as you have no idea of the underlying distribution of the data when given only the mean.

Is there any truth to the phrase "statistics mean nothing to the individual"?

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    $\begingroup$ This is overstatment, but you may find this talk interesting youtube.com/watch?v=LGqOH3sYmQA $\endgroup$ – Tim Oct 11 '18 at 12:36
  • $\begingroup$ The quotation harks back to a debate that spread throughout the social sciences from anthropometry to economics to psychology during the 19th century. At the beginning of that century, most scientists agreed with some proposition like this one: people are just too different and varied for statistical reasoning to be applicable to them. By the end of the century, the successes of innovators like Quetelet, Lexis, Fechner, and Galton had virtually eliminated that point of view. See Stigler, The History of Statistics. $\endgroup$ – whuber Oct 11 '18 at 16:31
  • $\begingroup$ While the statement is true, it is my opinion that statistics never claimed to perfectly predict individual cases. $\endgroup$ – Todd D Sep 19 '19 at 5:19

I think "nothing" is too strong, but I imagine the statement is a pedagogical challenge meant to address one or more issues:

I. It may be addressing the reification of statistical models.

II. As you say, it may be addressing point summaries, which do not necessarily represent any individual. (In fact, the summary value may be impossible for any individual to achieve.)

III. It may be emphasizing that probabilistic statements have a context. If you say "there's a 95% mortality rate for this disease" you're making a statement that marginalizes out all characteristics of patients except that they're human. In reality, a particular disease may affect men or women more, will affect the old, young, or middle more, will affect someone with a chronic disease or other pre-existing health issues more, will probably affect the never-exposed more than those who have previously been exposed (hence vaccines), will be more deadly if not treated or if not treated within an initial time window, ...

We're always leaving stuff out of predictions either because we don't have the information for the model we built or we don't have the information for the individual we're predicting on. In the best case, we lump all of the unknowns into an "error" term and if it's small enough and tame enough we ignore it. That's an ideal, though.

In light of that, saying "the disease kills 95% of humans who acquire it" is not the same as saying "the disease will kill you with 95% certainty".

We are only now getting to the place where medicine might be developed at the individual level and not the population level. The long list of side effects on medications is a testament to your slogan.

IV. It may be emphasizing that statistical machinery is not always necessary or useful. For example, if the question is "who is the tallest person in the class?" or "was our factory's production at an all-time high?", you don't need statistics. For this class or that factory, the data itself tells you and applying statistical machinery in that case is really more of a manipulation than a clarification.

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No, it's a statement made by people who don't understand probability.

If you contract a disease with a 95% mortality rate, you can't say you will certainly die.

But you absolutely can say "I will probably die." You can go further and say "The probability of my dying is 0.9." That's an awfully specific and highly informative statement.

People latch on to the idea that you can't assess people/objects on an individual level based on population statistics because it very quickly leads to uncomfortable situations such as profiling. But the idea that statistics don't matter on an individual level is absolute hogwash.

You cannot make definitive statements, but you can certainly make probabilistic ones.

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    $\begingroup$ In the particular case of contracting a disease, like you said, it seems sort of fair in some sense to say that you can't entirely assess an individual based on population statistics, since you mighn't be entirely comparable to the other subjects considered, where some may have been older or had pre-existing conditions that contributed, etc. This type of example seems less like more constrained examples, like a flip of a coin, where we can repeat the random independent event to assess accurately its randomness. $\endgroup$ – screeb Oct 11 '18 at 13:34

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