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If a test person is asked to raise one of his 10 fingers at a given signal, is the choice truly random if he counts in his mind from 1 to 10 and associates with each number one of his fingers? The 1 he associates with the left pink, the 2 with his left ring finger, 3 with his left middle finger, etc. So the test person starts to count, the experimenter gives him a signal, after which the test person raises the finger associated with the number he arrived at while counting. Let's suppose the signal is given at a random moment. Is the choice "in sync" with the random signal given?

In other words, if the experimenter records which finger is raised after each of a 1000 signals are given to a single person, will the experimenter see that each finger is raised the same number of times (more or less, because the number of signals given is finite; the more signals, the better you're getting at the real distribution)? So in the case of 1000 signals given to a test person will the experimenter record that each finger is raised about 100 times?

Or does the test person not make a choice at all?

Deschele Schilder
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I think your question ultimately is about whether people can or are able to behave like a uniform random number generator drawing numbers from 1 to 10. I don't think the fact that the participant needs to raise a finger changes things much.

Note that there is a distinction between what people do, and what people are capable of. A lot of research suggests that people are not very good at simulating randomness. That said, one can think of strategies that would allow a person to simulate randomness more effectively (e.g., drawing on sources of random information in the environment, or even applying a formula similar to that used to sequentially generate numbers using random number generators).

The broad question has already been posed on the site: How well can a human-generated "random number" be predicted?

I also note that a participant could just report sequentially 1,2,3..., 10, 1, ... This data would show 100 of each number for 1000 signals. Of course, this would exhibit structure that would not be present were each trial independent.

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Jeromy Anglim
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  • -Thanks for your clear answer! I see that you can as well tell the number you have in mind, instead of raising a finger, If the signal to tell which number you have in mind would be given at certain intervals, then counting to 10 over and over again obviously won't work. You would get the same result as in your last remark, and you'll become very predictable. I think the best way is to look at external stimuli, but then the question arises if it's you who makes the decision. – Deschele Schilder Feb 07 '17 at 08:19
  • @JeromyAnglim What kind of formula do you think is most effective? – ghosts_in_the_code Mar 05 '17 at 04:47
  • @ghosts_in_the_code presumably something that has good properties in terms of a random number generator but is easy for the human to calculate in their head. – Jeromy Anglim Mar 06 '17 at 00:24
  • @JeromyAnglim Yes, I was looking for some example of the same. Is there any SE where asking would be on-topic? – ghosts_in_the_code Mar 06 '17 at 03:53
  • In general, stats.stackexchange.com is a good place to ask questions about random number generators. – Jeromy Anglim Mar 06 '17 at 06:41