There is a corralation across the entire population that does not exist in 'bucket' of the population. More importantly, the bucketing involved is reasonable a

There is a corralation across the entire population that does not exist in 'bucket' of the population. More importantly, the bucketing involved is reasonable and has explanatory power. (If this were not the case, you might have picked the buckets specifically to get this result. Still an example of Simpsons Paradox, but not interesting.)