**Introduction**

Let’s say you have a hypothesis about an experiment that has only two possible outcomes, which you can code as 0 and 1. In Stata, you can easily identify the mean and 95% confidence interval (CI) of any binomial distribution. In this blog entry, we’ll show you how.

**Generate Data**

Let’s say that you polled 111 people on whether they would support the passage of a particular law, with support = 1 and opposition = 0. First, let’s create a dataset that reflects this experiment, and let’s add the gender of participants to demonstrate how Stata can subset binomial confidence intervals.

set obs 111

gen a_sup = runiform(0,1)

gen sup = round(a_sup)

label variable sup "Support"

label define sup 0 "Rejects" 1 "Supports"

label value sup sup

gen a_gender = runiform(0,1)

gen gender = round(a_gender)

label variable gender "Gender"

label define gender 0 "Male" 1 "Female"

label value gender gender

drop a*

codebook

**Generate the Binomial CI**

Now try the following code:

ci proportions sup

Here’s what you get:

So the proportion of people supporting the law is around 51.4%, and the 95% CI is around 41.7% to 61%. If you wanted, you could change the confidence level to 90% by trying:

ci proportions sup, level(90)

The confidence interval now becomes:

Let’s say you wanted to generate separate confidence intervals for men and women. Try the following code:

by gender, sort: ci proportions sup

Here’s what you get:

By the substantial overlap in CIs, you can infer that there is no statistically significant difference between male and female agreement with the law, but you might want to run a logistic regression with odds ratio reporting in order to confirm this intuition with a *p *value.

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