The Commons Year · Across the Table · for grown-ups
Across the Table
The case in three lines. The Green Gazette's summer league table says Hillside swimming club passes 70% of its swimmers and Riverside only 60%, and a parent moves her daughter. Split into beginners and improvers, Riverside does better in both groups, but three in four of its swimmers are beginners, so its total comes out lower. Riverside's coach writes in, and Tara has to write the corrections box.
One question to ask. "What should the box say?" Then: "So which club is better?" Let them argue it; it is harder than it looks.
One thing to do at the table. Make up two small teams on paper, one with mostly young players and one with mostly older ones, and give each player a score. Make the first team better in each age group but worse overall. If it works, you have built the paradox yourselves.
The grown-up layer. The case is about Simpson's paradox: a total can point the opposite way from every group inside it, when the groups are mixed in different amounts. It gives the young reporter his strongest point, that both percentages were correctly worked out. It gives the Hillside coach his: his swimmers really did pass. The habits it models are asking what a number is standing in for, going to the records that split the groups, and comparing like with like before ranking anything.
The case leaves the line blank on purpose. Ask for it before you offer yours.