Lecture 1: Observational studies and experiments

This lecture sets up the basics of randomized experiments, hypothesis testing, and data modeling. The next two lectures will then cover further methods for hypothesis testing and approaches to multiple hypothesis testing. They will build on the basic methods in this lecture to achieve better methodological accuracy and more generalizable models.

The discussion will be guided by a study conducted by the Health Insurance Program that offered mammographies for early detection of breast cancer, where the objective is to determine whether offering mammographies will lead to fewer deaths due to breast cancer. From this example, we will discuss two main considerations:

• the role of proper experimental design in setting up the study
• considerations for the data collection process in order to do valid inference

As you follow the discussion videos, your main take-away should not be particular details about this study. Rather, you should focus on developing an intuition on the important considerations for a study, as you may be conducting similar experiments or analyzing similar datasets of your interest in the future.

Lecture 2: Hypothesis testing

At the end of this lecture, you will be able to:

• Perform the Fisher Exact Test , and compute the p-value using the hypergeometric distribution .
• Apply the z-test and the t-tests on continuous data.
• Set up and perform hypothesis tests under assumptions and scenarios simular to the studies discussed.
• Choose appropriate test statistic for hypothesis tests and find their distributions.
• Discuss the usage and assumptions of the t-statistic and the t-distribution .
• Use various tests to evaluate whether a data set can be considered approximately normal .
• Compute a confidence interval for a parameter.

Lecture 3: Likelihood Ratio Test and Multiple Hypothesis Testing

At the end of this lecture, you will be able to

• Apply the Likelihood Ratio Test on the HIP mammography experiment and other similar scenarios.
• Define family-wise error rate (FWER) and false discovery rate (FDR) for a series of hypothesis tests and choose which of these to control in different scenarios of multiple hypothesis tests.
• Compute p-value corrections such as the Bonferroni correction and Holm-Bonferroni correction , to control the family-wise error rate (FWER).