Let's say I have two samples of results of two bernoulli experiments.H0:p1=p2H1:p1≠p2And I want to...

dotzis16xd

dotzis16xd

Answered

2022-03-24

Let's say I have two samples of results of two bernoulli experiments.
H0:p1=p2
H1:p1p2
And I want to try to reject H0 at a confidence level.
I already know a proper way to solve this, but I was wondering, if I have a confidence interval for p1 and p2, at the same level of significance. Can I just check if the intervals overlaps each other to test this?

Answer & Explanation

Korbin Ochoa

Korbin Ochoa

Expert

2022-03-25Added 11 answers

Step 1
Suppose the confidence intervals Ij have the property that pIj with probability 1α.
Then under the null hypothesis, pI1I2 with probability (1α)2=12α+α2, so this is a lower bound for the probability that I1 and I2 intersect.
Thus if they don't intersect, you can reject H0 with confidence level at most aαα2.
The true confidence level is presumably better than that, but without more analysis we don't know how much better.
Abdullah Avery

Abdullah Avery

Expert

2022-03-26Added 19 answers

It is true that if the intervals don't overlap, then there is a statistically significant difference. However, the converse is not true. Overlapping intervals do not imply that you cannot reject the null hypothesis.
The best approach to take is the one I'm assuming you've already done: Construct a confidence interval for the difference p1p2 and check to see if it contains the point 0 or not.

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