Simpson's Paradox Solution


Case 2

There are now 11 white and 9 black in the green container, while the orange has 12 white and 9 black. So orange is the one!

How can this be so? It seems impossible that we should need to switch. Impossible but true. To see why this is so consider:

Case 3

Suppose that the blue container has 7 white and 2 black, the red container 300 white and 100 black. The green has 8 white and 6 black, the orange has 8 white and 7 black.

Where would you pick from? Since 7/9 = 78% and 300/100 = 75% blue looks better than red again. Likewise, 8/14 = 57% and 8/15 = 53%, so again green looks better than orange.

If we pour the balls from the blue container into the green and those from the red one into the orange then the green has 15 white balls and 8 black, giving 65%, while the orange has 308 white and 107 black, giving 74%.

What has happened is that, relatively speaking, the red container has swamped the orange, so that the overall result in the orange is similar to what it was in the red. On the other hand, the blue and green containers hold similar numbers so they have averaged out.

Back to the question
Tad Boniecki

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