**Introduction**

Because of the special properties of a Poisson distribution, a special formula is applied to calculate a Poisson confidence interval. In this blog, you’ll learn how to calculate a Poisson confidence interval in Stata based on a known number of exposures and events.

**Poisson Confidence Interval**

Imagine that 10,000 people are exposed to a disease for which there are 4,000 deaths. In this example, the number of exposures is 10,000, and the number of events is 4,000. In order to calculate the Poisson confidence interval in Stata, try the following code:

cii means 10000 4000, poisson

Here’s what you get:

You can change the confidence level as follows:

cii means 10000 4000, level(90) poisson

Note that the Poisson 95% confidence interval is not the same as either an exact or a **Wald 95% confidence interval for proportions**. For example, try:

cii prop 10000 4000, exact

Note that the Poisson 95% confidence interval is broader. That’s also true of the Wald confidence interval for proportions:

cii prop 10000 4000, wald

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