Simpson's Paradox

Hans and Gretel were two perfectly normal and happy children, except that their parents were both statisticians. This led them to having certain unusual experiences with higher probability than other children who were not so blessed.

For example, one day Hans and Gretel were given some paint to play with. Hans got a thimble of white paint from his mother, and a very large bucket of pink from his father, a pink which was perfectly balanced between red and white. Gretel got a thimble of red paint from her father, and from her mother she got a very large bucket of paint that was almost entirely white, with only a single drop of red mixed in.

Hans and Gretel like tables, so they made one:

From Momthimble of whitebucket of 99% white, 1% red
From Dadbucket of pinkthimble of red

Hans and Gretel were about to mix their respective paints together when O.J. Simpson jumped out from behind a bush. "Eeek!" screamed the children.

"Don't worry", Mr. Simpson replied, "I'm just here to make a prediction; namely that Gretel's paints when mixed together will be redder than Hans's. For you see, your Mom gave redder paint to Gretel, and so did your Dad."

"Eeek!" screamed the children again, both because they were still scared of O.J. Simpson and because their parents had taught them to fear erroneous conclusions. But since their parents had also taught them the power of experimental verification, they mixed their respective paints together and lo and behold: Hans had a bucket of pink while Gretel had a bucket of only slightly pinkish white.

O.J. was so chastened by this empirical disproof that he immediately turned himself into the authorities and confessed all of his crimes. Hans and Gretel had many other adventures, but never once were they tempted into aggregating subpopulation statistics as if they were masses.