Patterns in Randomness

Abstract

Abstract I do an extra-sensory perception (ESP) experiment on the first day of my statistics classes. I show the students an ordinary coin— sometimes borrowed from a student—and flip the coin ten times. After each flip, I think about the outcome intently while the students try to read my mind. They write their guesses down, and I record the actual flips by circling H or T on a piece of paper that has been designed so that the students cannot tell from the location of my pencil which letter I am circling. Anyone who guesses all ten flips correctly wins a one-pound box of chocolates from a local gourmet chocolate store. If you want to try this at home, guess my ten coin flips in the stats class I taught in the spring of 2017. My brain waves may still be out there somewhere. Write your guesses down, and we’ll see how well you do. After ten flips, I ask the students to raise their hands and I begin revealing my flips. If a student misses, the hand goes down, Anyone with a hand up at the end wins the chocolates. I had a winner once, which is to be expected since more than a thousand students have played this game. I don’t believe in ESP, so the box of chocolates is not the point of this experiment. I offer the chocolates in order to persuade students to take the test seriously. My real intent is to demonstrate that most people, even bright college students, have a misperception about what coin flips and other random events look like. This misperception fuels our mistaken belief that data patterns uncovered by computers must be meaningful. Back in the 1930s, the Zenith Radio Corporation broadcast a series of weekly ESP experiments. A “sender” in the radio studio randomly chose a circle or square, analogous to flipping a fair coin, and visualized the shape, hoping that the image would reach listeners hundreds of miles away. After five random draws, listeners were encouraged to mail in their guesses. These experiments did not support the idea of ESP, but they did provide compelling evidence that people underestimate how frequently patterns appear in random data.