This unit continues the work of classical hypothesis testing. It builds on the work of the previous unit by asking questions about data that has more unique qualities than were covered in the previous unit. These unique qualities include:
- Pairings of data: When data has a logical pairing structure, it is possible to use this information to conduct a t-test that is uniformly better powered than without this pairing data. As a result, the deliberate data scientists can either detect smaller effects for the same budget, or can realize (potentially considerable) reductions in cost.
- Non-Metric data: When data does not contain metric information—that is, it is not interval or ratio data—there the t-tests that have been covered to this point are of no use. However, with the hypothesis-testing framework, it is possible to identify some other statistic that has a known distribution that works with lower-information data. In particular, this week will focus on (a) the sign-rank; and (b) the rank-sum tests.