> poisson.test(c(1, 11800), c(3, 1000000), alternative = c("two.sided"),conf.level = .93)
Comparison of Poisson rates
data: c(1, 11800) time base: c(3, 1e+06) count1 = 1, expected count1 = 0.035403, p-value = 0.03478 alternative hypothesis: true rate ratio is not equal to 1 93 percent confidence interval: 1.006334 146.142032 sample estimates: rate ratio 28.24859
Interestingly, if you multiply the CI I claimed before by the rate ratio instead of the expected rate, you get almost exactly the same CI as here.
> ci <- c(0.03562718, 5.17251332) > 28.24859 * ci [1] 1.006418 146.116208
> poisson.test(c(1, 11800), c(3, 1000000), alternative = c("two.sided"),conf.level = .93)
Comparison of Poisson rates
The lower bound of the CI approaches a rate ratio = 1 for a 93% confidence interval.Interestingly, if you multiply the CI I claimed before by the rate ratio instead of the expected rate, you get almost exactly the same CI as here.
* Note 11800 is about two years of pedestrian deaths and time units are in millions of miles. https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/...