Summary
If the expectations of two Poisson distributions are compared by means of the x 2-test, the probability of an error of the first kind is never much larger than the asymptotic value 0.01 or 0.02 or 0.05 on the three most usual levels.
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Egg, K., Rüst, H. & Van Der Waerden, B.L. Die Irrtumswahrscheinlichkeit des χ 2-Testes im Grenzfall der Poissonverteilung. Z. Wahrscheinlichkeitstheorie verw Gebiete 4, 260–264 (1965). https://doi.org/10.1007/BF00533757
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DOI: https://doi.org/10.1007/BF00533757