Chapter 2 Hypothetical repeated sampling and the t-test

This chapter introduces some of the foundational ideas behind hypothesis testing in the frequentist framework. The key idea is that of hypothetical repeated sampling. When we fit a model to a given data-set, we are assuming that this is one of potentially infinite numbers of exact repetitions of an experiment. We will leverage some amazing properties of these exact repetitions in order to draw inferences from our particular data. The key idea to understand here is the central limit theorem, which we will discuss below. Before we do that, it is useful to introduce some terminology relating to typical experiment designs in linguistics and psychology.