I have two independent populations with size n1=272 and n2=664. The number of successes are x1=4 and x2=6 respectively.

Is it statistically correct to use binom.dist() function to test the equality of two population proportions? In particular, can I obtain the p-value of the hypothesis test as follows:


or in general,

  • $\begingroup$ When you write "to test the two population proportions", you ought to clarify what is the actual hypothesis you wish to test. When you say you have two "populations" with size n1=272 and n2=664, are these actually the whole populations, or are they merely samples from those populations? $\endgroup$
    – Silverfish
    Aug 30 '16 at 10:15

That is not a correct way to test the equality of the proportions.

It takes as the population parameter to test against a sample proportion, ignoring the fact that it too is a random variable.

There are a variety of tests used for this situation, but a chi-squared test of homogeneity of proportions (equivalent to a test of independence) should do adequately (the most common rule people use would say that at just under 3 one of the expected values is too small - but the usual rule is a little bit too strict).


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