Lesson 3: Confidence intervals and how to read them correctly

A confidence interval (CI) is a range of values built from sample data by a procedure that, repeated many times, produces intervals capturing the true population parameter (for example, a mean or a proportion) a set percentage of the time. For example, a 95% confidence interval for the mean height of students might look like this: [172 cm, 178 cm]. The key question: what does “95%” mean? The correct answer: it's a property of the procedure in the long run. If we repeatedly take samples and build a 95% CI each time, about 95% of those intervals will capture the true value of the parameter. For an interval that's already been built, talking about probability is incorrect: the parameter is a fixed (though unknown to us) constant, not a random variable. What's random is the interval itself — it changes from sample to sample. A common mistake: “There's a 95% probability that the true mean lies in the interval [172, 178].” This statement is wrong, because the parameter either lies in this interval or it doesn't — there's no probability involved. The correct way to put it: “The method for building this interval captures the true parameter 95% of the time.”