# 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.

• 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? – yyyy0000 Nov 26 '14 at 10:22
• @owlstead Sorry for late response. But I am not getting what exactly bmm6o and you are talking about. – yyyy0000 Nov 26 '14 at 10:23
• @ moderators: Could you migrate the question to math.stackexchange ? – yyyy0000 Nov 18 '19 at 11:33
• There is no such thing as "@moderators", you should flag your question to gain attention. – Maarten Bodewes Dec 18 '19 at 17:06

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.