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Richard Hardy
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There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.testpoisson.test in R and, originally, it was a one-sided test. It did not support two-sided tests. The second would be that the p-value and the interval are using different loss functions, but I would suspect that is not the case. You should submit a bug report.

There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-sided tests. The second would be that the p-value and the interval are using different loss functions, but I would suspect that is not the case. You should submit a bug report.

There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-sided tests. The second would be that the p-value and the interval are using different loss functions, but I would suspect that is not the case. You should submit a bug report.

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Dave Harris
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There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-sided tests. The second would be that the p-value and the interval are using different loss functions, but I would suspect that is not the case. You should submit a bug report.