I want to compare two groups of coin tosses with different number of tosses

Question

I have a list of results of two different groups of coin tosses generated by http://www.wolframalpha.com/input/?i=10+coin+tosses. But the number of tosses is different: There are 10 in one group and 100 in the other one. Could I use a particular statistical test to obtain comparisons between those groups? Could I test if these groups have equal results?

Answer 1

You could use a z-test to compare these. One thing to bear in mind is that the power of the test will not be optimized if the $n_j$'s are not equal. I discuss that issue in my answer here.

Answer 2

I don't know if this would be computationally equivalent to gung's answer or not, but you could also use logistic regression to predict the probability of heads based on the IV of the dataset source. Also, a $\chi^2$ test of independence or a Fisher's exact test could be used.