Introductory Statistics

Module 5: Advanced Inference

As we enter the final learning module for the course, we flip the coin from confidence intervals to hypothesis testing. Where confidence intervals are used to estimate a population parameter (or relationship between population parameters), a hypothesis test is a part of confirmatory analysis, where we are merely checking if the hypothesized claim is reasonable in light of our data.

This leads to the observation that confidence intervals and hypothesis tests are two sides of the same coin. If we reject a hypothesis, then the hypothesized value is not in the confidence interval.

Unfortunately, it does not always make sense to talk about confidence intervals. When there are more than two possible outcomes, what would a confidence interval describe? If we are comparing more than two mans, what would a confidence interval mean? In such cases, we resort to hypothesis tests.

Make no mistake about it. When possible, a confidence interval gives a lot more information than a mere hypothesis test. It gives a set of reasonable values for the parameter. A hypothesis test just says how likely that parameter value is.