This is incidentally another way of explaining the effect. Consider the standard diagram of the joint probability density and how it relates to correlation. Now take a bite out of the upper right corner of big X and big Y events: unless the joint density started in a really strange shape this will tend to make the correlation negative.
This is known as Berkson’s paradox and it is ubiquitous. A lot of people have written about it and its implications, e.g. Yvain (underlying reasons why anti-correlations arise are very similar).
This is incidentally another way of explaining the effect. Consider the standard diagram of the joint probability density and how it relates to correlation. Now take a bite out of the upper right corner of big X and big Y events: unless the joint density started in a really strange shape this will tend to make the correlation negative.
This is known as Berkson’s paradox and it is ubiquitous. A lot of people have written about it and its implications, e.g. Yvain (underlying reasons why anti-correlations arise are very similar).