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I'm looking for the name of a statistical test or method to compute the statistical probability that H0 : two distributions of boolean variables are the same.

In an example, let's say i have a weighted coin that have a bias. If you throw it, you have either heads (1) or tails (0) and you have with this coin 20% chance to get heads, and 80 to get tails. It exists other coins that can yields for example 40% chance heads and 60% chance tails, or whatever.

I would like to know a method or test to calculate the probability that i'd be wrong saying that an identically biased coin have been used to get two distributions of flip trials results.

I found this test but for paired data. Or in my case, i'd like to be able to test a distribution of 1000 coin flips with one coin to a distribution of 150 coin flips for the other, if i follow my example.

I looked aroung but i may lack some vocabulary to found what i'm looking for. And i lack knowledge on how to calculate weighted probabilities of probabilities, sadly...

Thanks for any help !

Osamoele
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    Google "test of proportions." There's plenty about this here on CV. – whuber Jul 04 '22 at 14:10
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    @whuber Thanks ! And also for the link to "Significance test for two groups with dichotomous variable". Seems to contain more than every info i need with an anwsome answer. – Osamoele Jul 04 '22 at 14:24

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