# How to test if two coins have different biases? [duplicate]

probably a noob question because I'm a noob.

I have two coins, A and B. For each coin I have a sample of the results I get by tossing it. My null hypothesis is that A has equal or higher probability to land on HEAD than B, but that probability is unknown (as well as B's probability). However, the data shows me that B seems to be more probable to land on HEAD. How can I test the null hypothesis?

It seems to me that a simple t-test won't work - A coin toss is Bernoulli distributed, and not normally distributed. I thought about dividing each sample to sub-samples, consider the ratio of HEADs in each subsample as a random variable that is distributed approximately like a normal variable, and then use t-test. However, this seems like a complicated (and inaccurate) solution for a basic (the most basic?) question.

bonus points: what's the effect size?

• Closely related to stats.stackexchange.com/questions/43748/… and stats.stackexchange.com/questions/46847/… Jan 7, 2013 at 20:17
• Nothing the matter with noobie questions. As proof, this one has been asked and answered in many forms here; e.g., stats.stackexchange.com/questions/7790/…. (Although it is correct that the binomial distribution governs individual outcomes, the proportions observed in the experiment will be very accurately described by a normal distribution unless those proportions are extreme (close to $0$ or $1$).) As far as effect size goes: if you aren't interested in the difference in proportions, how do you want to express it?
– whuber
Jan 7, 2013 at 20:17