Normal-approximation tests for a Poisson exposure model (source code)

= Normal-approximation tests for a Poisson exposure model

For testing $H_0:\theta=1$ against a larger alternative, approximate size-$0.05$ upper-tail tests reject when
$$
\widehat\theta_{MLE}>1+\frac{1.645}{\sqrt{S_1}}
$$
or, respectively,
$$
\widehat\theta_{LS}>1+1.645\frac{\sqrt{S_3}}{S_2}.
$$