Play · 8 min

Level Playing Field

Two people. Two completely different tests. One of them did better — but the two scores are not on the same scale, so comparing the numbers tells you nothing.

You get each test’s average and its standard deviation. Make the call, and then watch both distributions slide onto one shared ruler so you can see who was really further ahead.

The distributions come in every shape — skewed, symmetric, flat, two-peaked. It makes no difference. A z-score is just how many standard deviations above or below the mean something is, and that works whatever the shape.

Eleven rounds, and the gap gets narrower every time. Three of them make you work out both z-scores before you may choose. Fresh numbers on every play, nothing graded, and nothing sent to me.