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Two questions about randomness of data-sequences:

  1. Using a variant of run test like Wald–Wolfowitz to check randomness hypothesis for a one-sample data sequence, which yields a P value denoting the probability of randomness, can we conclude the degree of randomness by looking at the resultant P value. That is; can we say the higher the P value the more random is the sequence, and the smaller the P value the more non-random is the sequence?

  2. If this concept is true; the next question is: In terms of P values, how random are sequences generated by a typical human mind?

kjetil b halvorsen
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Manin
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    Hi, welcome. Ever heard of [entropy](https://en.wikipedia.org/wiki/Entropy) or [maximum entropy](https://en.wikipedia.org/wiki/Principle_of_maximum_entropy)? – Jim Mar 27 '19 at 19:33
  • Welcome Manin! Also have you ever heard of computational mechanics? Crutchfield, J. P., & Feldman, D. P. (2003). [Regularities Unseen, Randomness Observed: Levels of Entropy Convergence](https://arxiv.org/pdf/cond-mat/0102181). *Chaos*, 13(1), 25–54. – Alexis Mar 27 '19 at 20:31
  • A p-value depends on things like sample size, which by itself has nothing to do with what you want to measure. So use some measure meant for randomness, like entropy. – kjetil b halvorsen Feb 20 '22 at 23:52

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