Introduction

In this chapter we take the first step toward extending the simple statistical model (formalized in chapters 2−4) in directions which allow for dependence and heterogeneity. Both of these dimensions are excluded in the context of the simple statistical model because the latter is built upon the notion of a random sample: a set of random variables which are both Independent and Identically Distributed (IID). In this chapter we concentrate on the notion of dependence, paving the way for more elaborate statistical models in the next few chapters. We also extend the bridge between theoretical concepts and real data introduced in chapter 5, by introducing some additional graphical techniques.

The story so far

In chapter 2 we commenced our quest for a mathematical framework in the context of which we can model stochastic phenomena: phenomena exhibiting chance regularity. We viewed probability theory as the appropriate mathematical set up which enables one to model the systematic information in such phenomena. In an attempt to motivate this mathematical framework, we introduced probability theory as a formalization (mathematization) of a simple chance mechanism, we called a random experiment ℰ, defined by the following three conditions:

1. [a] all possible distinct outcomes are known a priori,

2. [b] in any particular trial the outcome is not known a priori but there exists a perceptible regularity of occurrence associated with these outcomes,

3. [c] it can be repeated under identical conditions.