Quote:
Originally Posted by Yoshi63
I ran 7 separate simulations of 1,000,000 trials and got an average of 1.437%.
Every simulation was between 1.435 - 1.439, so I don't think it's variance error. Interesting because we are quite close, but seems like at least one of us made some small mistake in the code. Or perhaps the randomness wasn't great. I used PHP "shuffle" to randomize.
Thanks for doing this!
Interesting results. They look a little strange to me since the spread "should" be larger over such simulations if totally random.
Let's do a quick calculation. Using the well-known formula for standard deviation of the number of successes in 1,000,000 binomial trials with a success probability of 1.437%, the standard deviation is around 119. Meaning that getting 7 "cases" all within 20 or so of the mean looks suspicious.
I just ran 10 one-million trial simulations for comparison. The number of successes I got were:
14,255
14,040
13,986
14,081
14,269
13,996
14,061
14,300
14,025
14,130
Taking the finite-adjusted standard deviation of these numbers yields 118 which is what we'd expect (whether we use 1.412% or 1.437%).
I have double-checked my simulation code and have not found any error, though it is notoriously difficult to find one's own errors of course.
To summarize, thanks for doing your simulations. I think we can take it as confirmation that the true probability OP is seeking is around 1.4%. It also looks like your "randomization" technique may not be truly random. (Not a knock on you but on the randomization technique used by the software that you are using.)
Thanks again.