If you take a bunch of random samples of a normal distribution, and only look at subsamples with median 2 sds out, in approximately ~0 subsamples will you find it equally likely to see + 0 sds and +4 sds.
Wait, are you claiming +0 SD is significantly more likely than +4 SD in a subsample with median +2 SD, or are you claiming that +4 SD is more likely than +0 SD? And what makes you think so?
The former. I think it should be fairly intuitive if you think about the shape of the distribution you’re drawing from. Here’s the code, courtesy of Claude 3.5. [edit: deleted the quote block with the code because of aesthetics, link should still work].
Wait, are you claiming +0 SD is significantly more likely than +4 SD in a subsample with median +2 SD, or are you claiming that +4 SD is more likely than +0 SD? And what makes you think so?
The former. I think it should be fairly intuitive if you think about the shape of the distribution you’re drawing from. Here’s the code, courtesy of Claude 3.5. [edit: deleted the quote block with the code because of aesthetics, link should still work].