Introductory Statistics: The Modelling Approach

Introductory Statistics offers a radical new approach to teaching the subject. Statistics, the author observes, is the study of variability, both systematic and random. Random variability is most easily described by a histogram; systematic variability is described by changes in the shape of histograms. A natural way to study these two types of variability is through log linear and logistic models. Once these basic principles of statistical modelling have been grasped, the problem of inference can be introduced through the likelihood function. Common approaches to calibrating the likelihood functions through significance tests and Bayes theorem are briefly presented. The student is then introduced to more sophisticated statistical models, including parametric distributions, which are classified in three discrete, normal and duration distributions. With this groundwork, linear regression and ANOVA models are introduced as special cases that describe how histograms change. The text concludes with selected topics in dependent data. Accessible to non-mathematicians, the book assumes little prior knowledge, although later chapters deal with fairly advanced models. It includes many practical examples and will serve as an excellent first introduction for both undergraduate and graduate students.