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Suppose I had two statistics and I were to construct confidence intervals off the two statistics, and that they overlap. From what I understand, we cannot make a statement about the difference between the two statistics in terms of significance.

Would this statement rely on the underlying distributions of the two statistics being the same? Can I compare confidence intervals with different sample sizes, sampling collection, etc?

user321627
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  • You cannot compare these, you have to compute their difference and compute the CI of the difference. – user2974951 Jun 22 '22 at 06:28
  • @user2974951 Not so fast. https://stats.stackexchange.com/a/18259/919 partially answers this question by showing a way of comparing two Student t confidence intervals of the mean. – whuber Jun 22 '22 at 12:11

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