Statistics - not the trump card you think
Most times I see someone use a statistical argument online, I shake my head and scroll down to the next post. Here's why.
Real-world situations usually have too many variables for statistics to be useful
Obviously, to use statistical data to establish that A and B are causally related you have to isolate A and B in your comparison. It won't do to sample a bunch of red squares and blue spheres and draw a conclusion about a difference between red and blue objects. But this is exactly what many statistical argments are.
I once argued with a Jordan Peterson acolytes about whether there are intrinsic psychological differences between men and women. The acolyte cited Peterson as his source for a study showing that in cultures that try to treat men and women as if they don't have intrinsic psychological differences, the differences become more extreme. I pointed out that even if his claim about the study was accurate, and *even if* we ignore the fact there are few if any cultures that fit that description and assume they examined multiple different such cultures, it's *still* a bad argument because the way a culture treats gender is never anything close to the only difference between it and another culture. A real society has *thousands* too many variables for this to be a reasonable argument. But he got mad at me for refusing to treat his "study" as instant proof of his claim and wouldn't continue the debate.
Statistics often measure the wrong thing
I've seen people argue for gun confiscation saying that America has more gun homicides per year than a bunch of other (smaller) countries who have stricter anti-gun laws... only to find out that they were measuring the gun death rate *as a flat number* rather than a proportion of each country's population. Of course America will have more gun homicides if you measure it that way because America has more people than those other countries.
(Not to mention that argument is atrocious anyway for, again, ignoring the thousands of other variables involved.)
Similar common fallacies to that conclusion include counting suicides and defensive killings of criminals in one country but not in the other, etc.
Who made the judgements?
This doesn't apply to all statistics, but for ones about things that not everyone can agree on the exact definition of, you run into an even bigger problem than any of the above. Example: a statistic that "70% of sexual harassers are male". Even if you can establish the reliability of the source and the relevance of the figure, you have to ask who decided which cases count as sexual harassment.
Statistics can have ambiguous implications.
Even if you prove there's a non-coincidental correlation between A and B, that doesn't prove that A is the cause of B. You still have to consider the possibility that B is the cause of A, or that a certain C that wasn't considered in the study causes both B and A, or that a combination of A and C is required to cause B.
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