# Minimum number of independent trials needed to detect a bias [closed]

Suppose, I suspect that the probability of occurrence of a particular bit as $0$ is $.558$. Since, it is not $.5$, so this is possibly a bias. Now, my question is:

What is the minimum number of independent trials I need to confirm my result?

I mean, observing this scenario for, say 100 times, must not be convincing. There should be a theoretical result regarding this. It would be very helpful if someone links such papers while answering.

What I am looking for is: Suppose I suspect a possible bias of $0.5 \pm x$, $x \in (0, .5]$. Then, at least, say $2^{1/x}$ trials are need to confirm my suspicion.

## closed as off-topic by CodesInChaos, e-sushi, tylo, Gilles 'SO- stop being evil', SethDec 2 '14 at 20:29

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• Is this just confidence intervals for a binomial distribution? – bmm6o Nov 25 '14 at 21:30
• @bmm6o I don't think so! Or, probably I am misunderstanding. Can you elaborate a bit? – pushpen.paul Nov 26 '14 at 10:22
• @owlstead Sorry for late response. But I am not getting what exactly bmm6o and you are talking about. – pushpen.paul Nov 26 '14 at 10:23

To detect a bias of $p(1+q)$ (where $p$ is the probability for an Uniform Random event), we need roughly $\dfrac{1}{pq^2}$ samples.