On Saturday, I posted a poll asking readers to simply pick a number between 1 and 20. I promised I’d explain what this is all about, so here goes.
The poll was inspired by this post on Pharyngula, which in turn was inspired by this article on Cosmic Variance. The idea is that 17 will always be the most common answer when people are asked to choose a number between 1 and 20. But neither Cosmic Variance nor Pharyngula offered a reasonable means of testing this proposition. That’s where our poll came in. This morning, I took a look at our data, and with 347 responses, I can confirm that 17 is significantly more popular than any number. Take a look at the chart:
As you can see, the number 17 was picked much more often — almost 18 percent of the time, compared to the 5 percent you might expect from this sample.
But even random numbers aren’t perfectly distributed — if you roll a die 6 times, you most likely won’t get one of each number. Perhaps in a truly random sample, we’d see a similar distribution. So I had my computer generate 347 random numbers in the same range and plotted them in light blue on the chart. Using the computer, the number 19 was most common, but it was chosen just 8 percent of the time. Humans picked the number 17 significantly more often than the computer picked 19.
Are there any other patterns in numbers humans “randomly” choose? Take a look at this chart:
Humans picked odd numbers significantly more often than the computer did. But how much of that effect is due simply to the larger “17 effect”? Consider this chart with the 17 data removed:
Now there is no significant difference between the values picked by humans or by the computer, and both results are no different than the theoretical “random” distribution of numbers.
What about prime numbers? Commenter Fletcher suggested that prime numbers seem more random, so they are more likely to be chosen. Here’s a chart of those results:
Yes, we do pick prime numbers more often than computers! A similar analysis, removing “17” from the results, diminished but did not eliminate the effect.
Clearly humans aren’t very good random number generators. We predictably select some numbers more than others. If I were to repeat this experiment with a naive audience, I’d very likely find “17” to be the most popular random number, but if I repeated it with the computer, a completely different number would most likely emerge as the preferred number.
Note: There is a wrap-up of all the reaction to this post here.