Simpson's Statistical Paradox: Results for a whole group may be the exact opposite of each part.
Simpson noticed a paradox in an earlier paper:
The death rate for African Americans was lower in Richmond than in New York.
The death rate for Caucasians was lower in Richmond than in New York.
The death rate for the total combined population of African Americans and Caucasians was higher in Richmond than in New York.
This paradox is explained by a mathematical quirk like this one: 1/5 < 2/8 and 6/8 < 4/5 but 7/13 > 6/13
This can lead to a result for the whole which is the exact opposite of the results for the smaller groups that make up the population.
It is complicated, but when you read conclusions based on statistics, beware that it is not always as clear cut as politicians and advocates would have you believe.