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I'm trying to compare the poll results to a truly random sample. Next this commenter is confused about why I say "truly random." The reason is that the poll results may or may not be truly random.
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When you say "If they were 'perfectly' distributed in this sense then they would hardly be random," you're saying the same thing I say: "even random numbers aren't perfectly distributed." Yes, this is true, but many people misunderstand what random numbers are, so I wanted to give a quick explanation of why random numbers do not, in small samples, evenly distribute themselves along each value. What does 'perfectly' distributed mean? If it means a sample in which data is distributed exactly as per expected values then why ever would someone say "even random numbers", If they were 'perfectly' distributed in this sense then they would hardly be random. I don't have a Reddit account, so I'll answer some of the questions in the discussion thread here. Note: There is a wrap-up of all the reaction to this post here. 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. We predictably select some numbers more than others. 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.Ĭlearly humans aren't very good random number generators. What about prime numbers? Commenter Fletcher suggested that prime numbers seem more random, so they are more likely to be chosen. 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.
![pick a number between 1 and 3 10 times pick a number between 1 and 3 10 times](https://hi-static.z-dn.net/files/dc1/275c020ba36d41c553ecbaec3c9a37c3.png)
But how much of that effect is due simply to the larger "17 effect"? Consider this chart with the 17 data removed: Humans picked odd numbers significantly more often than the computer did. Humans picked the number 17 significantly more often than the computer picked 19.Īre there any other patterns in numbers humans "randomly" choose? Take a look at this chart: Using the computer, the number 19 was most common, but it was chosen just 8 percent of the time. So I had my computer generate 347 random numbers in the same range and plotted them in light blue on the chart. Perhaps in a truly random sample, we'd see a similar distribution. Take a look at the chart:Īs 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.īut even random numbers aren't perfectly distributed - if you roll a die 6 times, you most likely won't get one of each number. 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. But neither Cosmic Variance nor Pharyngula offered a reasonable means of testing this proposition. The idea is that 17 will always be the most common answer when people are asked to choose a number between 1 and 20. The poll was inspired by this post on Pharyngula, which in turn was inspired by this article on Cosmic Variance. I promised I'd explain what this is all about, so here goes. On Saturday, I posted a poll asking readers to simply pick a number between 1 and 20.