These tools depart from rigorous theorems in mathematical statistics but are immensely useful in practice. They provide empirical evidence to improve a statistical model and fit in nicely with Box’s …

Models with linear predictors form the basis of most applied statistical analyses. It is often the case, though,thatthereisnoscientificreasontobelievetheselinearmodelsaretrueforagivenapplication.

Data-based model selection How does using the data to select among models affect statistical inference? Data-based sampling procedures How does the protocol for collecting data observations …

Figure 1.1 illustrates the general, abstract flow of a statistical analysis, starting from a hypothesis and ending at the communication of the scientific conclusion.

Types of statistical models Several statistical models are commonly used, each suited for different types of data and research questions:

Statistical models are idealizations, postulated by statisti-cians — needed to be verified. For example, the data histograms should look like theoretical distributions.

It is often stated in statistics that: No model is right but some models are useful. In this chapter we will: define what we mean by a statistical model; give a range of examples.