The Univariate Fallacy is the claim that if there is no single, defining trait that can be used to separate two or more categories, then those categories do not exist.
Univariate statistics work fine when applied to univariate problems, but when you use them on multivariate problems they fail.
For example, “there is no single, category defining trait that separates chimp and human brains”, which is true, becomes a fallacy if you used it to say that it doesn’t make sense to talk about chimp and human brains being different categories.
You would think this was obvious, but there are a number of examples of this in research papers. Most recently, it is used to “prove” that it doesn’t make sense to categorise humans as male or female, because there is no single biological measure that can be used. This is true, but when you consider it a multivariate problem, the problem is much easier to solve. There are two main categories (male and female) and an extremely small group that is neither – this last group does not invalidate the main categories.
And if you are really good, you can even get your own variant of the Univariate Fallacy named after you, something that Richard Lewontin managed to do. Lewontin tried to show that there it didn’t make sense to talk about genetic differences between human populations – and therefore that no specific traits could be inherited in those populations – and tried to do that as an univariate problem. This is now known as Lewontin’s Fallacy.
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