Let's suppose I have two treatments, A and B, that I use on randomly sampled individuals of a population. I want to assess the relation between the treatment and the probability of an event happening to an individual.

I treat 95 individuals with A, and the event happens to 1. I treat 115 indivuals with B, and the event happens to 2 of them.

First of all am I right to use the chi-squared independance test to test if the probability of the event occuring is the same whatever the treatment?

Second of all, given that the test tells me there is no significative difference, I want to assess how powerful this test is. How do I calculate how likely I am to find an effect if I assume that one group is twice as likely to encounter the event than another?



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