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I have two independent experiments

In experiment 1, I perform n1 trials, and I have s1 successes.

In experiment 2, I perform n2 trials, and I have s2 successes.

How do I find out (without conducting more trials) whether it's significantly more likely that a trial in experiment 1 succeeds than that a trial in experiment 2 succeeds?

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  • $\begingroup$ As a self-comment, right now I'm primarily interested in the answer to the question, but answers that also help me find how I can solve these kinds of problems are greatly appreciated. Not sure if that means I should tag this as self-study or not. $\endgroup$
    – Martijn
    Commented Nov 26, 2016 at 14:49

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Putting $p_1 = \frac{s_1}{n_1}, p_2 = \frac{s_2}{n_2}$ this answer is exactly what you need.

For more tests like this you can take a look at the wikipedia page of Statistical hypothesis testing.

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You compute the difference between the two estimated proportions and test that the true difference is statistically greater than 0.

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