Significance tests are everywhere: they are used across the sciences to evaluate probabilistic hypotheses. But they are controversial: some people even claim that the tests are bunk and should be given up. This course will describe how significance tests work: we will focus on Fisher tests, but may touch on Neyman-Pearson tests if there's time. And we will discuss some objections to significance testing: e.g. sensitivity to the stopping rule, sensitivity to the test statistic, and how a well-supported hypothesis may be rejected.

I have three red hats and two white hats. I put a hat on Alice, on Bob, and on Cat. I ask each in turn if she knows the color of her own hat. Alice says she doesn't know. Bob says he doesn't know. Cat says she doesn't know. What color is Cat's hat? This course will be an introduction to epistemic logic, a powerful and general framework for representing people's states of mind, e.g. their beliefs, their beliefs about the others' beliefs, their beliefs about the others' beliefs about the others' beliefs, and so on, all the way up. The framework will solve all our puzzles. But, more than that, we will point towards some applications of the framework in computer science, game theory and philosophy.