Inferential Statistics

Confidence Interval

The confidence interval is the best way to holistically consider our inference about the population.

On the standard error page of this site, I described how to use a standard error to calculate a confidence interval for a mean:

confidence interval = observed mean ± 2 * standard error

The confidence interval represents the influence of sampling error on our population inference. (Recall that sampling error is the unavoidable uncertainty we have because we're making an inference based on a sample rather than the entire population.) When using the formula above, we are 95% confident that the true population value falls within the confidence interval.

Does the population value actually and truly fall within the confidence interval? No one knows. Unless we decide to pony up the resources to measure the entire population, no one will ever know. But at least we know, courtesy of the field of statistics, how uncertain we should be about the whole thing.

In other words, if we were to assume the population is exactly the way our sample is, that certainty would be an illusion. There is inevitable uncertainty in our estimate because we're only using a sample. The confidence interval helps us avoid kidding ourselves about how certain our estimates are.