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I have two groups of samples with a proportion of mutations in each sample being a particular type (the proportions are represented as a fraction of 1). How to I check if that type of mutation is significantly likelier to happen in one group over the other?

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Partially answered in comments:

You could use a χ2 test for proportions. – user25658 If you want to be able to consider both one- and two- tailed tests, what about a two-sample proportions test? – Glen_b

See also What is the relationship between a chi squared test and test of equal proportions?

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