Take a 1000 marbles, different sizes. Colour them randomly, red or blue. Throw them in a bag.
Take 100 marbles. Colour the largest halve red, the other halve blue. Add them to the bag.
Statistically, with sufficient sampling, an outsider will be able to measure the difference in average size, red group of marbles vs blue group of marbles.
But if you’re a marble meeting another marble, knowing their assigned colour gives you very little information on if they’re bigger or smaller than you.
Take a 1000 marbles, different sizes. Colour them randomly, red or blue. Throw them in a bag.
Take 100 marbles. Colour the largest halve red, the other halve blue. Add them to the bag.
Statistically, with sufficient sampling, an outsider will be able to measure the difference in average size, red group of marbles vs blue group of marbles.
But if you’re a marble meeting another marble, knowing their assigned colour gives you very little information on if they’re bigger or smaller than you.