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Let us say we define telepathy as mental awareness of existing physical data without using physical senses. I would like to determine the existence of such ability in a statistically significant way. I am neither a statistician or mathematician so would like to know how proof of the following conditions would be statistically significant:
I design a program to randomly generate a number between 1 and 3
Chance determination of that number without looking would be 33%

I know there is something called p-value for significance and that 0.05 is considered significant in most accepted peer-reviewed studies so that is the pvalue I want to achieve.

How many correct values in a dataset of 100 numbers will I need to achieve pvalue 0.05?

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(too long for a comment)

http://www.aaas.org/aaas-affiliates lists the Parapsychological Association as an affiliate, confirming that the American Association for the Advancement of Science regards parapsychology as a valid field of study, though that doesn't mean they accept it as truth.

Your question is fairly basic (no offense) and could've been asked without the first paragraph. In general, you'd expect 33.33... correct with a variance of 100*(1/3)*(2/3) or 200/9 for a standard deviation of about 4.7. 0.05 requires 2 SDs, so if you got 33.333+2*4.7.. rounded up to 43 or more correct, you'd have 0.05. However, there are many other factors to consider before claiming success.

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  • $\begingroup$ True. Anyway, be aware that getting 43 right out of 100 is not an strong result. Furthermore, trying rounds of 100 sets of questions until one of them gives 43 or more right results is not a significant result. $\endgroup$ – Pere Dec 18 '16 at 15:58
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Funny you should ask. In an infamous article published in the Journal of Personality and Social Psychology, Bem (2011) did that: he argued that some significance tests achieving $p < .05$ constituted evidence of the existence of psychic powers. Among the many objections critics raised is that extraordinary claims require extraordinary evidence; see, for example, the Bayesian approach taken by Wagenmakers et al. (2011). Whatever the exact reason, I think that most psychologists and statisticians (not to mention physicists) would agree that you would be insane to walk away from the Bem study believing that psychic powers are real.

More generally, I'd recommend availing yourself of the voluminous existing literature on parapsychology, particularly experiments like this, before doing your own study. I can't think of a topic less deserving of new research.

Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100, 407–425. doi:10.1037/a0021524

Wagenmakers, E. J., Wetzels, R., Borsboom, D., & van der Maas, H. L. (2011). Why psychologists must change the way they analyze their data: The case of psi: Comment on Bem (2011). Journal of Personality and Social Psychology, 100, 426–432. doi:10.1037/a0022790

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  • $\begingroup$ I realize in science the majority of believers accept the results of others without testing it in their own experience and I also realize when dealing with deterministic physical data it is completely rational to so. $\endgroup$ – Anoop Alex Dec 18 '16 at 8:07
  • $\begingroup$ however in the case of consciousness i prefer to test and know myself than simply accept the beliefs of another person's experience. $\endgroup$ – Anoop Alex Dec 18 '16 at 8:09
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    $\begingroup$ Read David J Hand,s book "The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day.". He deals with this issue and many others. He is a famous British statistician who has published several books and numerous articles on probability and statistics. $\endgroup$ – Michael R. Chernick Dec 18 '16 at 14:41
  • $\begingroup$ By the way I do not see the logic behind the answer of @barrycarter. $\endgroup$ – Michael R. Chernick Dec 18 '16 at 14:44
  • $\begingroup$ The paper "Statistical aspects of ESP" (1940) Journal of Parapsychology by this famous statistician also looks interesting. (Though I could not find it online, so have not read it.) $\endgroup$ – GeoMatt22 Dec 18 '16 at 16:24

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