We became suspicious of the number of clean sweeps in The Price Is Right when there were not the expected six of them in 6,000 episodes. The chance there would be only one was about one and a half percent, not very high. But are there so few clean sweeps that we should be suspicious? That is, is the difference between the expected number of sweeps and the observed number so large as to be significant? Is it too big to just result from chance?

This is significance testing: is whatever quantity we mean to observe dramatically less than what is expected? Is it dramatically more? Is it at least different? Are these differences bigger than what could be expected by mere chance? For every statistician’s favorite example, a tossed fair coin will come up tails half the time; that means, of twenty flips, there are expected to be ten tails. But there being merely nine or as many as twelve is reasonable. Three or fifteen tails may be a little unlikely. Zero or twenty seem impossible. There’s a point where if our observations are so different from what we expect then we have to reject the idea that our observations and our expectations agree.

It’s not enough to say there’s a probability of only 1.5 percent that there should be exactly one clean sweep episode out of 6,000, though. It’s unlikely that should happen, but if we look at it, it’s unlikely there should be *any* outcome. Even the most likely result of 6,000 episodes, six clean sweeps, has only about one chance in six of happening. That’s near the chance that the next person you meet will have a birthday in either September or November. That isn’t absurdly unlikely, but, the person betting against it has the surer deal.

Continue reading “The First Tail”

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