Introductory statistics: the modelling approach

Abstract

Statistics is the study of variability, both systematic and random. Randon variability is most easily described by a histogram and systematic variability 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 by the student, 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: parametric distributions, classified into three groups, discreet, normal and duration distributions. With this groundwork, linear regression and ANOVA models are introduced as special cases of describing how histograms change. In a final chapter, selected topics in dependent data, from strehastic processes are presented. This book is intended for first introduction to statistics for any student at undergraduate or graduate level; of particular interest to non-mathematicians.