I want to create a simple project to show about ESP.
I started with the idea of guessing whether a coin would be heads or tails.
I first wanted to show some values by pure guessing.
So, using random numbers of zero (tails) or heads (one), I generated 1000 pairs of these and put them in the first two columns of a spreadsheet. If the two values in the pair matched, I recorded it as a correct guess (a one in the third column of the spreadsheet) and if they didn't match, a zero.
I found the mean of the third column. It was approximately 0.5.
Then I took the standard deviation of this third column also. It's value was also close to 0.5 (about 0.49 or so).
I then took the mean plus two times the standard deviation which got me a value of about 1.5.
I did this because I was thinking this would show more than two standard deviations from the mean, which would be 95%. My idea was if someone could guess correctly above two standard deviations from the mean, that this would suggest unusual ability better than randomly guessing.
Then I realized that, for example, if someone guessed correctly ten times, that would be an average of 1 (from 10 / 10). But that will be less than 1.5 (the value from the mean of the random numbers plus two times their standard deviation). It would always be impossible to guess heads/tails and get 1.5 or better.
My friend suggested that I have to take the standard deviation value divided by the square root of 1000 (the number of trials). I don't know if this suggestion is right or not. If I do this, double it, and add it to the mean, I get a value of about 0.55. This suggests if a person guesses more than 55% correctly, this is above two standard deviations. I don't know if this is the right way or not, and why.