Imagine you have a study that finds 66.6% of women love cats.

Now imagine you meet a woman. What are the odds that she loves cats?If you know nothing about her, you’d be tempted to give the answer “66.6%.” And you would be wrong. If asked, “does she love cats?” you might be tempted to answer Yes, on the generalization that women love cats and the observation that she is a woman. You might be right or wrong.

This is a common cognitive error among human beings that I see playing out here every day, so it’s worth exploring what it is and why it’s erroneous.The Law of Large Numbers states that the greater the sample, the more likely the results are to resemble expected values. The inverse is just as true, The Law of Small Numbers: the smaller the sample, the less predictable the results.

The study from which you learned that 66.6% of women love cats could be immaculately designed, with a large random, or representative, sample of 10,000 female respondents. But the woman you just met is effectively 1 respondent. The margin of error of the study might be insignificant, just a percentage point or two in either direction. But if you do the math on the same data with sample of n=1, the margin of error is necessarily much larger. Often, in social science research, it is much larger than the difference between your initial results (n=10,000) and a coin-flip. In fact, the effect of sample size on margin of error is greater than the effect of proportional representation. So even predictions which take into account some variables of representation— like “Gen Z” or “white”--don’t do as much as you’d think to improve your odds of guessing correctly on an individual level.

This simple and introvertible fact about how math works is part of the science of statistics employed by social science research. Ignoring it would therefore completely invalidate the claim that we are “following the science.” Yet ignoring it is what we do every time we apply population-wide generalizations to individual behavior.

The fact is that you don’t know the odds that a given woman loves cats. You can’t even make an educated guess without knowing other facts about her, by which point you’re already engaged in a much more complex process than generalization.Think about this the next time someone posts a youtube video or links an anecdote from another sub, or asks the question “How does bluepill explain THIS?” or when you feel the urge to predict misery in an individual man or woman's future.

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PS: There are innumerable occasions in everyday life where we need to make snap decisions on limited information where we might rely on generalizations. No one denies that. I am not, for instance, going to wander into a large group of tough-looking men for directions under the statistically true fact that the majority of young men in the region are not violent. However, we are not doing “life” on this sub—we are doing amateur sociology. Might as well be a little better at it.

PPS: Flaired "bluepill discussion" because insofar as anything can be called bluepill, discouragement of overgeneralization should make the top of the list.